Tvm Pv, Fv Send
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The Time Value of Money Which would you rather have – Rs. 10,000/Today or Rs. 10,000/- in 5 years? Obviously, Rs. 10,000/- today. today Money received sooner rather than later allows one to use the funds for investment or consumption purposes. This concept is referred to as the TIME VALUE OF MONEY!! MONEY
Compound Interest (Single Period) When interest is paid on not only the principal amount invested, but also on any previous interest earned, this is called compound interest. FV = Principal + (Principal x Interest) = 2000 + (2000 x .06) = 2000 (1 + i) = PV (1 + i) Note: PV refers to Present Value or Principal
Future Value (Graphic) If you invested Rs. 10,000 today in an account that pays 6% 6 interest, with interest compounded annually, how much will be in the account at the end of two years if there are 0 no withdrawals?1 2
6%
Rs.10,000 FV
Future Value (Formula) FV1 = PV (1+i)n = Rs. 10,000 (1.06)2 = Rs. 11,236/FV = future value, a value at some future point in time PV = present value, a value today which is usually designated as time 0 i = rate of interest per compounding period n = number of compounding periods
Future Value (Casio Financial Calculator) Go to CMPD Menu Set : END
N
2
I % Yr
6
PV
-10,000
FV
11,236
Future Value Example Ram wants to know how large his Rs. 50,000 deposit will become at an annual compound interest rate of 8% at the end of 5 years. years
0
8%
1
2
3
4
5
Rs.50,000/-
FV5
Future Value Solution Calculation based on general formula: FVn = PV (1+i)n FV5 = Rs. 50,000 (1+ 0.08)5 = Rs. 73,466.40 Calculator Key Strokes : PV = - 50,000/I =8% N = 5 yrs FV = 73,466.40
Double Your Money!!! Quick! How long does it take to double Rs.5,000 at a compound rate of 12% per year (approx.)?
We will use the “Rule-of-72”.
The “Rule-of-72” Quick! How long does it take to double Rs.5,000 at a compound rate of 12% per year (approx.)? Approx. Years to Double = 72 / i% 72 / 12% = 6 Years [Actual Time is 6.12 Years]
Future Value Q1. Mr. X invests Rs.25000 in a deposit paying interest at 10% per annum compounding yearly. What will he get on maturity after 10 years?
Set=begin N=10 i=10 Pv=-25000 Fv=solve=64843.5615
Future Value Q.2.Naman deposits Rs.100000/- in a bank that pays 8% interest compounded annually. How much the deposit will grow after 5 years and 8 years respectively?
• Answer: • For 5 years FV = Rs.146932.8077(n=5,i=8,pv=-100000, fv=solve • For 8 years FV = Rs.18509.30
Q.3 Nisha deposit Rs.80000/- in a bank at 10% interest compounding semi-annually. How much deposit will grow after 5 years?
• • • • • • •
Answer: Set=begin N=5 i=10 Pv=-80000 c/y=2 Fv=solve=130311.5701
Q.4 Mr. X takes a loan of Rs.145000/- from Mr. Y. Y is charging an interest rate of 8.5% per annum compounded quarterly from X. How much interest Y gets if X pay back loan in 5 years?
• • • • • • •
Sol. Set = begin N=5 i=8.5 Pv=145000 c/y=4 Fv=solve=-220805.2489 Interest = 220805-145000=75805
Q.5 Nisha invest in a fixed deposit of Rs.180000/- @ 12% p.a. compounded monthly. What will be the amount she will get after 2.8years?
• • • • • • •
Sol. Set=begin N=2.8 i=12 Pv=-180000 c/y=12 Fv=solve=251461.015
Q.6 Deepti Gupta Invest Rs.20000 at 12% p.a. compounded half yearly. Calculate the amount she has after 2 years 5 months?
• • • • • • •
Sol. Set=begin N=2+5/12 i=12 Pv=-20000 c/y=2 Fv=solve=20985.37
Q.7 Shikha won the lottery worth Rs.960000/-. She invests this amount in a term deposit at 9.5%. Compounding is done annually for the 1st year and quarterly for the 2rd year. Calculate the amount she has after 2 years?
• • • • • • •
Sol. Step1 Set=begin N=1 i=9.5 Pv=-960000 Fv=1051200
step 2 set=begin n=1 i=9.5 pv=-1051200 c/y=4 fv=1154678.319
Q.8 Meenakshi invest Rs.200000/- for 4 years in a term deposit of a bank at 6% p.a. compounded semi-annually. After 4 years she deposit half the maturity proceeds in post office at a rate of 7% per annum compounded quarterly for 6 years and from the rest of the maturity proceeds she buys the Handy Cam for her daughter. Calculate the money she has after 10 years?
• • • • • • • •
Sol. Step 1 Set=begin N=4 i=6 Pv=-200000 c/y=2 Fv=solve=253354.0163 fv=solve=384196.8704
Step 2 set= begin n=6 i=7 pv=-253354.0163/2 c/y=4
Q.9 Suman has Rs.260000/- if she invest Rs.145000 in a term deposit of bank earning 8% p.a. compounding quarterly and balance in a post office saving scheme earning 8.5% p.a. compounded semi annually. Calculate the amount she has after 2 years 9 months? =
• • • • • • • • •
Sol. Step 1 Step 2 Set = begin set=begin N=2+9/12 n=2+9/12 i=8 i=8.5 Pv=-145000 pv=-(260000-145000) c/y=4 c/y=2 Fv=solve fv=solve=144582.6533 =180289.2747 Total amount = 180289.2747+144582.6533 = 324871.928
Q10. Mr. Ambani deposits Rs.5 lakh in a account that gives interest at 13% p.a. compounded monthly for 1st year, 12% p.a. for 2nd year and after that 10% p.a. compounded quarterly forever. Find the maturity amount after 10 years?
Present Value • Since FV = PV(1 + i)n. PV = FV / (1+i)n. • Discounting is the process of translating a future value or a set of future cash flows into a present value.
Present Value (Graphic) Assume that you need to have exactly Rs.40,000 saved 10 years from now. How much must you deposit today in an account that pays 6% interest, compounded annually, so that you reach your goal of Rs. 40,000?
0
6%
5
10
Rs.40,000 PV0
Present Value (Formula) PV0 = FV / (1+i)10 = Rs.40,000 / (1.06)10 = Rs.22,335.80
0
6%
5
10
Rs.40,000 PV0
Present Value (Casio Financial Calculator) Go to CMPD Menu
N
10
I
6
FV
40,000
PV
- 22,335.80
Present Value Example Ram needs to know how large of a deposit to make today so that the money will grow to Rs.50,000 in 5 years. Assume today’s deposit will grow at a compound rate of 4% annually.
0
4%
1
2
3
4
5
Rs.50,000 PV0
Present Value Solution Calculation based on general formula: PV0 = FVn / (1+i)n PV0 = Rs.50,000/(1.04)5 Rs.41,096.35
=
Present Value (Casio Calculator) Go to CMPD Menu
N
5
I
4
FV
50,000
PV
41,096.35
Present Value Q.1 What amount need to be invested now to have Rs.21435.88 in 8 years given an annual rate of interest of 10% p.a. compounding yearly ?
Answer: Rs.10000
Q.2 What amount needs to be invested today to have Rs.800000 after 12 years if the investment earns 10% rate of return compounding monthly?
Answer: Rs.242156.4784
Q.3 What amount must be invested @ 8%p.a. for 4 years compounded semi-annually to grow to Rs.100000/-?
Answer: Rs.73069.02
Q4. What would you prefer Rs.5000 today or Rs. 7000 after 6 years. Assuming that Rs. 5000 can be invested for 6 years at 9% p.a. compounding annually. Answer: Value of Rs. 5000 after 6 years is Rs. 8385.50 which is more than Rs. 7000 receivable after 6 years. So better take Rs. 5000 today.
Q5. Which option is better: b. 1 lac today c. 50000 now and 60000 thousand after 2 years d. 30000 now, 35000 after 2 years and 45000 after 4 years If discount rate is 14% p.a. compounded quarterly?
Q.6. What amount must be invested @ 8%p.a. for 4 years compounded quarterly to grow to Rs.10000/-?
Answer: Rs.7284.45
Q.6 Nitin wants to accumulate Rs.150000 in 3years for one month trip to USA assuming he can get 8% annual return on her investments compounded quarterly. How much he invests today in order to achieve her goals. Answer: Rs.118273.97
Q.7 Manish wants to accumulate Rs.150000 in 3 years for one month trip to USA assuming he can get 8% annual return on his investments compounded monthly. How much he invests today in order to achieve his goal. Answer: Rs.118088.19
Q.8 How much you invest now to have Rs.100000 after 2 years if the interest for the first year is 5%p.a and for the second year 6.5%p.a compounding annually. Answer: Rs.89425.43
Q.9 How much you invest now to have Rs.100000 after 2 years if the interest for the first year is 5%p.a compounding annually and for the second year 6.5%p.a compounded semi annually? Answer: Rs.89336.83
Q.10 What amount need to be invested now to get Rs.30474/- after 2 years if you get Rs.18662 from a term deposit of bank earning 8% p.a. compounding annually and balance in a post office saving scheme earning 8.5% p.a. compounded semi annually. Answer: Rs.26000 (Approx) Step 1:-
N=2 I=8 FV= 18662 PV= solve=15999.65
Step2:-
N=2 I= 8.5 FV =(30474-18662) = 11812 c/y=2 PV=solve=10000.44
Compound Interest (Single Period) When interest is paid on not only the principal amount invested, but also on any previous interest earned, this is called compound interest. FV = Principal + (Principal x Interest) = 2000 + (2000 x .06) = 2000 (1 + i) = PV (1 + i) Note: PV refers to Present Value or Principal
Future Value (Graphic) If you invested Rs. 10,000 today in an account that pays 6% 6 interest, with interest compounded annually, how much will be in the account at the end of two years if there are 0 no withdrawals?1 2
6%
Rs.10,000 FV
Future Value (Formula) FV1 = PV (1+i)n = Rs. 10,000 (1.06)2 = Rs. 11,236/FV = future value, a value at some future point in time PV = present value, a value today which is usually designated as time 0 i = rate of interest per compounding period n = number of compounding periods
Future Value (Casio Financial Calculator) Go to CMPD Menu Set : END
N
2
I % Yr
6
PV
-10,000
FV
11,236
Future Value Example Ram wants to know how large his Rs. 50,000 deposit will become at an annual compound interest rate of 8% at the end of 5 years. years
0
8%
1
2
3
4
5
Rs.50,000/-
FV5
Future Value Solution Calculation based on general formula: FVn = PV (1+i)n FV5 = Rs. 50,000 (1+ 0.08)5 = Rs. 73,466.40 Calculator Key Strokes : PV = - 50,000/I =8% N = 5 yrs FV = 73,466.40
Double Your Money!!! Quick! How long does it take to double Rs.5,000 at a compound rate of 12% per year (approx.)?
We will use the “Rule-of-72”.
The “Rule-of-72” Quick! How long does it take to double Rs.5,000 at a compound rate of 12% per year (approx.)? Approx. Years to Double = 72 / i% 72 / 12% = 6 Years [Actual Time is 6.12 Years]
Future Value Q1. Mr. X invests Rs.25000 in a deposit paying interest at 10% per annum compounding yearly. What will he get on maturity after 10 years?
Set=begin N=10 i=10 Pv=-25000 Fv=solve=64843.5615
Future Value Q.2.Naman deposits Rs.100000/- in a bank that pays 8% interest compounded annually. How much the deposit will grow after 5 years and 8 years respectively?
• Answer: • For 5 years FV = Rs.146932.8077(n=5,i=8,pv=-100000, fv=solve • For 8 years FV = Rs.18509.30
Q.3 Nisha deposit Rs.80000/- in a bank at 10% interest compounding semi-annually. How much deposit will grow after 5 years?
• • • • • • •
Answer: Set=begin N=5 i=10 Pv=-80000 c/y=2 Fv=solve=130311.5701
Q.4 Mr. X takes a loan of Rs.145000/- from Mr. Y. Y is charging an interest rate of 8.5% per annum compounded quarterly from X. How much interest Y gets if X pay back loan in 5 years?
• • • • • • •
Sol. Set = begin N=5 i=8.5 Pv=145000 c/y=4 Fv=solve=-220805.2489 Interest = 220805-145000=75805
Q.5 Nisha invest in a fixed deposit of Rs.180000/- @ 12% p.a. compounded monthly. What will be the amount she will get after 2.8years?
• • • • • • •
Sol. Set=begin N=2.8 i=12 Pv=-180000 c/y=12 Fv=solve=251461.015
Q.6 Deepti Gupta Invest Rs.20000 at 12% p.a. compounded half yearly. Calculate the amount she has after 2 years 5 months?
• • • • • • •
Sol. Set=begin N=2+5/12 i=12 Pv=-20000 c/y=2 Fv=solve=20985.37
Q.7 Shikha won the lottery worth Rs.960000/-. She invests this amount in a term deposit at 9.5%. Compounding is done annually for the 1st year and quarterly for the 2rd year. Calculate the amount she has after 2 years?
• • • • • • •
Sol. Step1 Set=begin N=1 i=9.5 Pv=-960000 Fv=1051200
step 2 set=begin n=1 i=9.5 pv=-1051200 c/y=4 fv=1154678.319
Q.8 Meenakshi invest Rs.200000/- for 4 years in a term deposit of a bank at 6% p.a. compounded semi-annually. After 4 years she deposit half the maturity proceeds in post office at a rate of 7% per annum compounded quarterly for 6 years and from the rest of the maturity proceeds she buys the Handy Cam for her daughter. Calculate the money she has after 10 years?
• • • • • • • •
Sol. Step 1 Set=begin N=4 i=6 Pv=-200000 c/y=2 Fv=solve=253354.0163 fv=solve=384196.8704
Step 2 set= begin n=6 i=7 pv=-253354.0163/2 c/y=4
Q.9 Suman has Rs.260000/- if she invest Rs.145000 in a term deposit of bank earning 8% p.a. compounding quarterly and balance in a post office saving scheme earning 8.5% p.a. compounded semi annually. Calculate the amount she has after 2 years 9 months? =
• • • • • • • • •
Sol. Step 1 Step 2 Set = begin set=begin N=2+9/12 n=2+9/12 i=8 i=8.5 Pv=-145000 pv=-(260000-145000) c/y=4 c/y=2 Fv=solve fv=solve=144582.6533 =180289.2747 Total amount = 180289.2747+144582.6533 = 324871.928
Q10. Mr. Ambani deposits Rs.5 lakh in a account that gives interest at 13% p.a. compounded monthly for 1st year, 12% p.a. for 2nd year and after that 10% p.a. compounded quarterly forever. Find the maturity amount after 10 years?
Present Value • Since FV = PV(1 + i)n. PV = FV / (1+i)n. • Discounting is the process of translating a future value or a set of future cash flows into a present value.
Present Value (Graphic) Assume that you need to have exactly Rs.40,000 saved 10 years from now. How much must you deposit today in an account that pays 6% interest, compounded annually, so that you reach your goal of Rs. 40,000?
0
6%
5
10
Rs.40,000 PV0
Present Value (Formula) PV0 = FV / (1+i)10 = Rs.40,000 / (1.06)10 = Rs.22,335.80
0
6%
5
10
Rs.40,000 PV0
Present Value (Casio Financial Calculator) Go to CMPD Menu
N
10
I
6
FV
40,000
PV
- 22,335.80
Present Value Example Ram needs to know how large of a deposit to make today so that the money will grow to Rs.50,000 in 5 years. Assume today’s deposit will grow at a compound rate of 4% annually.
0
4%
1
2
3
4
5
Rs.50,000 PV0
Present Value Solution Calculation based on general formula: PV0 = FVn / (1+i)n PV0 = Rs.50,000/(1.04)5 Rs.41,096.35
=
Present Value (Casio Calculator) Go to CMPD Menu
N
5
I
4
FV
50,000
PV
41,096.35
Present Value Q.1 What amount need to be invested now to have Rs.21435.88 in 8 years given an annual rate of interest of 10% p.a. compounding yearly ?
Answer: Rs.10000
Q.2 What amount needs to be invested today to have Rs.800000 after 12 years if the investment earns 10% rate of return compounding monthly?
Answer: Rs.242156.4784
Q.3 What amount must be invested @ 8%p.a. for 4 years compounded semi-annually to grow to Rs.100000/-?
Answer: Rs.73069.02
Q4. What would you prefer Rs.5000 today or Rs. 7000 after 6 years. Assuming that Rs. 5000 can be invested for 6 years at 9% p.a. compounding annually. Answer: Value of Rs. 5000 after 6 years is Rs. 8385.50 which is more than Rs. 7000 receivable after 6 years. So better take Rs. 5000 today.
Q5. Which option is better: b. 1 lac today c. 50000 now and 60000 thousand after 2 years d. 30000 now, 35000 after 2 years and 45000 after 4 years If discount rate is 14% p.a. compounded quarterly?
Q.6. What amount must be invested @ 8%p.a. for 4 years compounded quarterly to grow to Rs.10000/-?
Answer: Rs.7284.45
Q.6 Nitin wants to accumulate Rs.150000 in 3years for one month trip to USA assuming he can get 8% annual return on her investments compounded quarterly. How much he invests today in order to achieve her goals. Answer: Rs.118273.97
Q.7 Manish wants to accumulate Rs.150000 in 3 years for one month trip to USA assuming he can get 8% annual return on his investments compounded monthly. How much he invests today in order to achieve his goal. Answer: Rs.118088.19
Q.8 How much you invest now to have Rs.100000 after 2 years if the interest for the first year is 5%p.a and for the second year 6.5%p.a compounding annually. Answer: Rs.89425.43
Q.9 How much you invest now to have Rs.100000 after 2 years if the interest for the first year is 5%p.a compounding annually and for the second year 6.5%p.a compounded semi annually? Answer: Rs.89336.83
Q.10 What amount need to be invested now to get Rs.30474/- after 2 years if you get Rs.18662 from a term deposit of bank earning 8% p.a. compounding annually and balance in a post office saving scheme earning 8.5% p.a. compounded semi annually. Answer: Rs.26000 (Approx) Step 1:-
N=2 I=8 FV= 18662 PV= solve=15999.65
Step2:-
N=2 I= 8.5 FV =(30474-18662) = 11812 c/y=2 PV=solve=10000.44
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