Business And Financial Mathematics - Interest Calculation
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Interest Sub Topics I Definition of Interest II Simple Interest III Compound Interest IV Application in business V. Problems
I
Definition of Interest If we save or invest our money in a bank we are getting a revenue from the bank for a certain period. The revenue we get from our investment is called interest.
II Simple Interest Simple Interest Formula I=PRt Where: I = Interest P =Principal R = interest rate per time unit (month) t = time Pt = P + I = P + PRt = P(1+Rt) Where Pt = Total amount over t months. Example. A man invested Rp 200.000 at 1,5% per month simple interest. Find the total amount for 8 months. Answer. Given P=200,000, R=0,015, t = 8 Pt = 200,000(1+0,015x8) =200,000x 1,12 = 224,000
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III Compound Interest Compound Interest Formula Pt = P(1+i)t Where i = interest rate Example. A man invested Rp 200.000 at 1,5% per month compounded monthly Find the total amount for 8 months. Answer. Given P=200,000, R=0,015, t = 8 Pt = 200,000(1+0,015)8 =200,000x 1.126493 =225,298.5 IV Application Example 1 A man invested at a bank Rp 500.000 at 1% per month compounded monthly. Find how much the interest over a year. Answer. Given P=500,000, i=0.01, t =12 I = Pt - P = 500,000(1+0,01) 12 - P =500,000x 1.126825 - 500.000 = 563,412.5 –500,000 =63,412.5 Example 2 A man invested at a bank 2 years ago Rp 800.000 at interest rate compounded monthly , amount of his investment is Rp 991.923. How much interest rate per month? Answer. Given P=800.000, t =24, Pt = 991.923 Pt = P(1+i)t 991.923 = 800.000(1+i)24 (1+i)24 = 991.923/800.000 (1+i) =( 991.923/800.000) 1/24 (1+i) =1,009 I =0,009 = 0,9%
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V Problems Problem1 When a man deposited at a bank Rp 400,000, the bank paid 1% per month compounded monthly. 6 months later, the bank paid 1.1% per month compounded monthly. Find the total amount for 2 years.? Problem2 A man deposited at a bank Rp 1000,000, the bank paid 1% per month compounded monthly. 8 months later, he added his deposits Rp 2,000,000. Find the total amount for 3 years?
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I
Definition of Interest If we save or invest our money in a bank we are getting a revenue from the bank for a certain period. The revenue we get from our investment is called interest.
II Simple Interest Simple Interest Formula I=PRt Where: I = Interest P =Principal R = interest rate per time unit (month) t = time Pt = P + I = P + PRt = P(1+Rt) Where Pt = Total amount over t months. Example. A man invested Rp 200.000 at 1,5% per month simple interest. Find the total amount for 8 months. Answer. Given P=200,000, R=0,015, t = 8 Pt = 200,000(1+0,015x8) =200,000x 1,12 = 224,000
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III Compound Interest Compound Interest Formula Pt = P(1+i)t Where i = interest rate Example. A man invested Rp 200.000 at 1,5% per month compounded monthly Find the total amount for 8 months. Answer. Given P=200,000, R=0,015, t = 8 Pt = 200,000(1+0,015)8 =200,000x 1.126493 =225,298.5 IV Application Example 1 A man invested at a bank Rp 500.000 at 1% per month compounded monthly. Find how much the interest over a year. Answer. Given P=500,000, i=0.01, t =12 I = Pt - P = 500,000(1+0,01) 12 - P =500,000x 1.126825 - 500.000 = 563,412.5 –500,000 =63,412.5 Example 2 A man invested at a bank 2 years ago Rp 800.000 at interest rate compounded monthly , amount of his investment is Rp 991.923. How much interest rate per month? Answer. Given P=800.000, t =24, Pt = 991.923 Pt = P(1+i)t 991.923 = 800.000(1+i)24 (1+i)24 = 991.923/800.000 (1+i) =( 991.923/800.000) 1/24 (1+i) =1,009 I =0,009 = 0,9%
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V Problems Problem1 When a man deposited at a bank Rp 400,000, the bank paid 1% per month compounded monthly. 6 months later, the bank paid 1.1% per month compounded monthly. Find the total amount for 2 years.? Problem2 A man deposited at a bank Rp 1000,000, the bank paid 1% per month compounded monthly. 8 months later, he added his deposits Rp 2,000,000. Find the total amount for 3 years?
22
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