Compound Interest

1) Compound Interest: For interest compounded a certain number of times, n, per year, such as monthly or quarterly, the formula is: •

t = Total time in years

•

n = Number of compounding periods per year (note that the total number of compounding periods is )

•

r = Nominal annual interest rate expressed as a decimal. e.g.: 6% = 0.06

2)find the interest rate per period:

2) find the number of interest periods required to achieve your goal:

3)Doubling The number of time periods it takes for an investment to double in value is

Shortcut to Calculation. Here is an Example to solve easily:

What will Rs.1500 amount to in three years if it is invested in 20% p.a. compound interest, interest being compounded annually? (1) 2400 (2) 2592 (3) 2678 (4) 2540 Correct Answer - (2) Solution:

The usual way to find the compound interest is given by the formula A = In this formula, A is the amount at the end of the period of investment P is the principal that is invested r is the rate of interest in % p.a And n is the number of years for which the principal has been invested.

.

In this case, it would turn out to be A = So great. How do you find the value of the above term? It is time consuming. Let us look at another alternative. What happens in compound interest? Interest is paid on interest. In the first year, interest is paid only on the principal. That is very similar to simple interest. However, from the second year onwards things change. In the second year, you pay interest on the principal and also interest on interest. Therefore, the Amount at the end of 2nd year in compound interest can be computed as follows 1 * Principal + 2* Simple interest on principal + 1 * interest on interest. Similarly, if you were to find the Amount at the end of 3 years in compound interest use the following method 1*Principal + 3 * Simple interest on principal + 3 * interest on interest + 1 * interest on interest on interest Let us see how it works in our example. The principal is Rs.1500. The rate of interest is 20%. Therefore, the simple interest on principal is 20% of 1500 = Rs.300 The interest on interest = 20% interest on the interest of Rs.300 = 20% of Rs.300 = Rs.60. Interest on interest on interest = 20% of Rs.60 = Rs.12. Now add all these Amount at the end of 3 years = 1*Principal + 3 * Simple interest on principal + 3 * interest on interest + 1 * interest on interest on interest = 1500 + 3*300 + 3*60 + 1*12 = 1500 +900 + 1800 +12 = 2592. You will get the same answer if you had used the formula. However, the calculation in this case was far easier than using the formula. Try out the same method for four and five years and remember the 1-2-1, 1-3-3-1, 1-4-6-4-1 etc method which you can use comfortably in the exam.

Simple and compound interest test Question 1 of 25 compound interest on Rs. 480 at 16 2/3% per annum for 2 3/4 years is:

1. Rs. 260 2. Rs. 252 3. Rs. 255 4. Rs. 263.33

Mark for revision | Unmark Question 2 of 25 Dhiraj invests a part of Rs. 8000 at 4% p.a. & the remainder at 5% per year. His annual income from the investments is Rs. 350. How much has he invested at each rate? (in rupees) 1. 3000, 4000 2. 5000, 3000 3. 3000, 5000 4. 4500, 5000

Mark for revision | Unmark Question 3 of 25 A sum of Rs. 2600 is lent in two parts in such a way that the interest on one part at 10% for 5 years is equal to that on another part at 9% for 6 years. The sum lent out at 10% is :

1. Rs. 1250 2. Rs. 1350 3. Rs. 1150 4. Rs. 1450

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Question 4 of 25 The simple interest on a sum of money for 2 years is Rs. 100 and the compound interest on the same sum at the same rate for the same time is Rs. 104. The rate of interest is:

1. 2% p.a. 2. 11/13% p.a. 3. 4% p.a. 4. 8% p.a.

Mark for revision | Unmark Question 5 of 25 Ram’s capital exceeds Shyam’s capital by of Shaym’s capital. Shyam invests his capital at C.I. for 3 years at 5% per annum. At what rate % per annum at S.I. must Ram invest his capital in older that at the end of 3 years, the two amounts are the same?

1. 1.67 2. 1.37 3. 2.21 4. None of these

Mark for revision | Unmark Question 6 of 25 A owes B Rs. 456.75 payable 4 months hence and B owes A Rs. 455.51 payable 3 months hence. If they agree to settle their account by a ready money payment, what sum should be paid over and to whom, reckoning the rate of true discount at 4 percent per annum?

1. Rs. 2 paid to A 2. Rs. 1 paid to A 3. Rs. 2.5 paid to B 4. Rs. 3 paid to B

Mark for revision | Unmark Question 7 of 25 A certain sum is invested for certain time. It amounts to Rs. 80 at 5% per annum. But when invested at 2% per annum, it amounts to Rs. 40. Find the sum and the time?

1. Rs. 26.67, 100 years 2. Rs. 13.33, 50 years 3. Rs. 13.33, 100 years 4. Rs. 21.33, 100 years

Mark for revision | Unmark Question 8 of 25 Raghav obtains Rs.1100 after lending out Rs. x at 5% per annum for 2 years and obtains Rs. 1800 after lending out Rs. y at 10% per annum for 2 years. Find the value of x + y?

1. Rs. 2100 2. Rs. 2200 3. Rs. 2500 4. Rs. 2600

Mark for revision | Unmark Question 9 of 25 If the difference between compound interest and simple interest on a certain amount, for two years is Rs. 7.35, find the principal, if the rate of interest is 7%?

1. Rs. 1500 2. Rs. 1200 3. Rs. 1480 4. Rs. 620

Mark for revision | Unmark Question 10 of 25 A sum of money at compound interest amounts in two years to Rs. 3630, and in three years to Rs. 3993. Find the original sum?

1. Rs. 3000 2. Rs. 2500 3. Rs. 2800 4. Rs. 3200

Mark for revision | Unmark Question 11 of 25 The simple interest on a certain sum of money for 4 years at 4 per cent per annum lags the compound interest on the same sum for 2 years at 10 per cent, per annum by Rs. 60. Find the sum?

1. Rs. 1400 2. Rs. 1200 3. Rs. 1500 4. None of these

Mark for revision | Unmark Question 12 of 25 The C.I. and simple interest on certain sum for 2 years are respectively Rs. 41 & Rs. 40. Find the sum & rate per cent?

1. Rs. 400, 5% 2. Rs. 450, 3% 3. Rs. 500, 4% 4. None of these

Mark for revision | Unmark Question 13 of 25 Divide Rs. 3903 between A & B such that A’s share at the end of 7 years is equal to B’s share at the end of 9 years at 4% p.a. rate of compound interest?

1. Rs. 2233, 1670 2. Rs. 2125, 1778 3. Rs. 2075, 1828 4. Rs. 2028, 1875

Mark for revision | Unmark Question 14 of 25 Simple interest on a certain sum at a certain rate is 9/16 of the sum. If the number representing rate percent and time in years be equal, then find the rate?

1. 7½% 2. 7% 3. 8% 4. 8.5%

Mark for revision | Unmark Question 15 of 25 A sum of money is invested at compound interest payable annually. The interest in successive years was Rs. 225 and Rs. 238.50. Find the rate % p.a.?

1. 5% 2. 6.5% 3. 5.5% 4. 6%

Mark for revision | Unmark Question 16 of 25 Nishit deposited a certain sum of money in a post office at 10% p.a. for 4 years & deposited an equal amount in a fixed deposit in a bank for 5½ years at 11% p.a. If the difference in the interest from the two sources is Rs. 563.75, find the sum deposited.

1. Rs. 2250 2. Rs. 2450 3. Rs. 2550 4. Rs .2750

Mark for revision | Unmark Question 17 of 25 A sum of money lent out at simple interest amount to Rs. 680 after 3 years and to Rs. 980 after a further period of 5 years. Find the rate %?

1. 8.5 % 2. 8 % 3. 7.8% 4. 12%

Mark for revision | Unmark Question 18 of 25 Out of a certain sum, is invested at 4%, th at 5% and the rest at 10%. If the simple interest for 3 years from all these investments amounts to Rs. 900, find the original sum?

1. Rs. 5000 2. Rs. 5100 3. Rs. 4500 4. Rs. 4900

Mark for revision | Unmark Question 19 of 25 Amit invested two equal sums of Rs. 5000 for 2 years at 10% C.I. – one at C.I. payable yearly and other at C.I. payable half yearly. Find the difference in amounts that he will get at the end of 2 years.

1. Rs. 23.50 2. Rs. 24.50 3. Rs. 25.50 4. Rs. 27.50

Mark for revision | Unmark Question 20 of 25 Mr. X invested a sum at C.I. pay payable half yearly in May and November. If the C.I. in November, 2003 was Rs. 225 and in May 2004 it was Rs. 236.25, then find the annual rate of interest?

1. 7% 2. 8% 3. 9% 4. 10%

Mark for revision | Unmark Question 21 of 25 A tractor is sold for Rs. 450000 cash or Rs. 150000 cash down payments together with ten equal monthly installments of Rs. 32000 each. Find the rate of interest charged under the investment plan.

1. 12.38% 2. 13.38% 3. 14.38 %

4. 15.38%

Mark for revision | Unmark Question 22 of 25 A lent B Rs. 900 for a certain time at a certain rate percent per annum, which is equal to the square root of the number of the months of the time. After the time B wanted to return the money, but A instead of taking the interest which amounted to Rs. 48 asked for a certain sum of money at the same rate for a certain number of years which is equal to the square root of the rate percent. Find the sum of money so that none of them should be the loser? (Take simple interest)

1. Rs. 620 2. Rs. 540 3. Rs. 600 4. Rs. 580

Mark for revision | Unmark Question 23 of 25 A sum of money is accumulating at compound interest at a certain rate of interest. If simple interest instead of compound were reckoned, the interest for the first two years would be diminished by Rs. 20 and that for the first three years, by Rs. 61. Find the sum.

1. Rs. 7500 2. Rs. 7000 3. Rs. 6500 4. Rs. 8000

Mark for revision | Unmark Question 24 of 25 Raghav has to repay a loan of Rs. 12,820 in three annual payments; the first payment being half of the second and one third of the third. If the C.I. is calculated annually at rate of 10%, then find the value of the third payment that Raghav has to make?

1. 5324

2. 6934 3. 7986 4. 8986

Mark for revision | Unmark Question 25 of 25 A certain sum of money when deposited in a post–office, becomes 7/5 of itself in 8 years. An equal sum deposited in a fixed deposit in a bank doubles itself in 12 1/2 years. Which of the two agencies the post office or the bank gives a better rate of interest?

1. the bank 2. the post 3. both are equal 4. cannot say . Simple and compond interest Question 1 of 25 Robin lend out Rs. 9 on the condition that the loan is payable in 10 months by 10 equal installments of Re. 1 each. Find the rate of interest per annum.

1. 22 % 2. 25 % 3. 26 % 4. 28 % Question 2 of 25 A loan of Rs. 2000 is to be paid back in 3 equal annual installments. How much is each installment, to the nearest whole rupee, if the interest is compounded annually at 12½ % p.a.?

1. Rs. 750 2. Rs. 790 3. Rs. 810

4. Rs. 840

Question 3 of 25 A milk man borrowed Rs. 2, 500 from two money lenders. For one loan, he paid 5% p.a. and for the other, he paid 7% p.a. The total interest paid for two years was Rs. 265. How much did he borrow at 5% and 7% respectively?

1. Rs. 2125, Rs. 575 2. Rs. 2275, Rs. 425 3. Rs. 2125, Rs. 375 4. None of these

Question 4 of 25 A sum of Rs. 1230 is borrowed at 5% C.I. interest for 2 years on the condition that it is refunded in 2 equal installments- one at the end of the first year & the other at the end of the second. Find the amount of each installment?

1. Rs. 637.50 2. Rs. 655.50 3. Rs. 661.50 4. None of these

Question 5 of 25 Simple interest on a certain sum of money for 4 years at 4% per annum exceeds the compound interest on the same sum for 3 years at 5 percent per annum by Rs. 228. Find the sum

1. Rs. 96000. 2. Rs. 86000 3. Rs. 81000 4. Rs. 91000

Question 6 of 25 Three persons Amar, Akbar and Anthony invested different amounts in a fixed deposit scheme for one year at the rate of 12% per annum and earned a total interest of Rs. 3,240 at the end of the year. If the amount invested by Akbar is Rs. 5000 more than the amount invested by Amar and the amount invested by Anthony is Rs. 2000 more than the amount invested by Akbar, what is the amount invested by Akbar?

1. Rs. 12,000 2. Rs. 10,000 3. Rs. 7,000 4. Rs. 5000

Question 7 of 25 A certain amount compounded annually after 10 years becomes 5120 and after 16 years becomes 10,000. What was the original amount?

1. Rs. 1677 2. Rs. 1177 3. Rs. 2077 4. Rs. 2177

Question 8 of 25 Vankatlal takes money from the employees cooperative society at lower rate of interest and saves in a scheme, which gives him a compound interest of 20%, compounded annually. Find the least number of complete years after which his sum will be more than doubled?

1. 2 years 2. 4 years 3. 6 years 4. 8 years

Question 9 of 25 The S.I. on a certain amount will be of the principal after a certain number of years. If the interest is Rs. 385.50 at the end of the second year, find rate of interest per annum?

1. 15% 2. 14% 3. 13% 4. Data Insufficient Question 10 of 25 Ram invests a certain amount of money and earns a Compound Interest of Rs. 420 in the second year and a C.I. of Rs. 462 in the third year. Calculate at what rate of interest did Ram invest?

1. 9% 2. 10% 3. 11% 4. None of these Question 11 of 25 A man borrowed same money every year at 10% C.I. If at the end of 3 years, he pays Rs. 2641, how much money had he borrowed each year?

1. Rs. 695.25 2. Rs. 725.35 3. Rs. 755.45 4. None of these

Question 12 of 25 A money lender borrows money at 4% per annum and pays the interest at the end of the year. He lends it at 6% p.a. compounding half-yearly & receives the interest at the end of the year. In this way he gains Rs. 104.50 in that year. How much money does he borrow?

1. Rs. 4850 2. Rs. 4500 3. Rs. 5000 4. Rs. 5200 Question 13 of 25 Find the present worth of Rs. 481.25 due 2 years hence, reckoning simple interest at 4 percent per annum. Also, what is the discount?

1. Rs. 437.50, Rs. 43.75 2. Rs. 437, Rs. 42.15 3. Rs. 481.25, Rs. 44.75 4. Rs. 560.875, Rs. 45.25

Question 14 of 25 Mr. X, a very industrious person, wants to establish his own unit. For this he needs an instant loan of Rs. 5,00,000 and, every five years he requires an additional loan of Rs. 100,000. If he had to clear all his outstanding in 20 years, and he repays the principal of the first loan equally over the 20 years, find what amount he would have to pay as interest on his initial borrowing if the rate of interest is 10% p.a. simple Interest?

1. Rs. 560,000 2. Rs. 540,000 3. Rs. 525,000 4. Rs. 500,000

Question 15 of 25 Sam buys a house for Rs. 23000. There is a ground rent of Rs. 500 a year, and annual repairs come on an average to 1½% on the purchase price of the house. At what monthly rent must he leave the house so as to get a return of 8% per annum on the purchase price?

1. Rs. 215.50 2. Rs. 223.75 3. Rs. 227.25 4. Rs. 231.50

Question 16 of 25 Two equal sums are lent at the same time at 9% and 8% simple interest respectively. The former is recovered 6 months earlier than the later, and the amount in each case is Rs. 17680. Find the times for which they are lent. (in years)

1. 3, 3½ 2. 3½, 4 3. $4, 4½ 4. 5, 5½ 5. 4, 5½

Question 17 of 25 A sum of money at C.I. doubles in 1 year. In how many years will it amount to 8 times itself?

1. 8 2. 16 3. $10 4. 3 5. 7

Mark for revision | Unmark Question 18 of 25 The sum is invested at compound interest payable annually. The interest in two successive years starting from first year was Rs. 500 and Rs. 540. The sum is :

1. Rs. 5600 2. Rs. 3750 3. Rs. 6250 4. Rs. 5000 Question 19 of 25 A father left a will that his capital of Rs. 18750 should be divided between his two sons aged 12 years and 14 years respectively, so that when they attained majority at the age of 18 years; the amounts received by each at 5% simple interest were the same. Find the sum allotted to elder son?

1. Rs. 9750 2. Rs. 9450 3. Rs. 9000 4. Rs. 8700

Question 20 of 25 Two equal sums are lent at the same time at 6% and 5% simple interest respectively. The former is received 2 years earlier than the later, and the amount in each case is Rs. 2400. Find the sum?

1. Rs. 1500 2. Rs. 1550 3. Rs. 1750 4. None of these Seema closes her account in an investment option scheme by withdrawing Rs. 10,000. One year ago she had withdrawn Rs. 6,000. Two years ago she had withdrawn Rs. 5,000. Three years ago she had not withdrawn any money. How much money had she deposited (approx) at the time of opening the account 4 years ago, given the annual simple interest is 10%?

1. Rs. 19,690

2. Rs. 16,500 3. Rs. 15,600 4. Rs. 18,030 Question 22 of 25 The sum of Rs. 725 is borrowed at the beginning of a year at interest. After 8 months have passed Rs. 362 ½ more is borrowed at a rate of interest double that at which the former sum bears. At the end of the year, the sum of interest on both loans is Rs. 43.50. What is the first rate of interest per annum?

1. 3.5% 2. 4.5% 3. 5% 4. 5.5% Question 23 of 25 Divide Rs. 6000 into two parts so that S.I. on the first part for 2 years at 6% p.a. may be equal to the simple interest on the second part for 3 years at 8% p.a.

1. 4000, 2000 2. 3500, 2500 3. 3800, 2200 4. None of these Question 24 of 25 On a sum of Rs. 1000, the C.I. for 2 years is twice the S.I. for 2 years when the rate is 11%. Find the rate at which the interest is compounded annually? 1. 10% 2. 15% 3. 20% 4. 25%

Question 25 of 25 In order to buy a car, a man borrowed Rs. 180,000 on the condition that he had to pay 7.5% interest every year. He also agreed to repay the principal in equal annual installments over 21 years. After a certain number of years, however, the rate of interest has been reduced to 7%. It is also known that at the end of the agreed period, he will have paid in all Rs. 270,900 in interest. For how many years does he pay at the reduced interest rate?

1. 7 years 2. 12 years 3. 14 years 4. 16 years December 18, 2003: Peter invested a certain sum of money in a simple interest bond whose value grew to $300 at the end of 3 years and to $ 400 at the end of another 5 years. What was the rate of interest in which he invested his sum? Initial amount invested = $ X Amount at the end of year 3 = $ 300 Amount at the end of year 8 (another 5 years) = $ 400 Therefore, the interest earned for the 5 year period between the 3rd year and 8th year = $400 $300 = $100 As the simple interest earned for a period of 5 years is $ 100, interest earned per year = $20. Therefore, interest earned for 3 years = 3 * 20 = $ 60. Hence, initial amount invested X = Amount after 3 years – interest for 3 years = 300 – 60 = $ 240.

Rate of interest =

=

= 8.33%

January 20, 2004: Ann invested a certain sum of money in a bank that paid simple interest. The amount grew to $240 at the end of 2 years. She waited for another 3 years and got a final amount of $300. What was the principal amount that she invested at the beginning? The sum grew to $240 at the end of 2 years. At the end of another 3 years, the sum grew to $300. i.e. in 3 years, the sum grew by $60. Therefore, each year, it grew by $20. Sum at the end of 2 years = $240

Sum grew by $20 each year. Hence, in the first 2 years, sum grew by 2 * 20 = $40. Therefore, sum at the beginning of the period = Sum at the end of 2 years - $40= $240 - $40 = $200. March 29, 2004 : Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds? Explanatory Answer Shawn received an extra amount of ($605 - $550) $55 on his compound interest paying bond as the interest that he received in the first year also earned interest in the second year. The extra interest earned on the compound interest bond = $55 The interest for the first year = $

Therefore, the rate of interest =

= $275

= 20% p.a

20% interest means that Shawn received 20% of the amount he invested in the bonds as interest If 20% of his investment in one of the bonds = $275, then his total investment in each of the bonds =

= 1375

As he invested equal sums in both the bonds, his total savings before investing = 2*1375 = $2750.