Question

1.)Calculate the annual compound interest rate if you invest $100 today and the value grows to $120 two years from now. Two decimals, whole percent (e.g. 5.23).

2.)How many years will it take $100 to grow to $133.82, if annual compound interest is 6%? # no decimals

3.)Calculate the future value of $100 invested today for 3 years, where the nominal annual interest rate of 4% is compounded quarterly? To two decimals.

4.)Your friend borrowed $5,000 three years ago and promised to pay you back with 8% interest. No payments were made. How much money does he owe you today? No commas, two decimals.

Answer 1

1). Amount invested PV = $100

Final value FV = $120

time period of investment = 2 years

So, annual rate is calculated as

r = FV/PV)^(1/t) - 1 = (120/100)^(1/2) - 1 = 9.54%

annual compound interest rate = 9.54%

2). Amount invested PV = $100

Final value FV = $133.82

Interest rate = 6%

So, time is calculated using formula

t = Ln(FV/PV)/ln(1+r) - 1 = Ln(133.82/100)/Ln(1.06)-1 = 4 years

3). amount invested PV = $100

time period = 3 years

rate r = 4% compounded quarterly

So, n = 4 quarter in a year

So, FV = PV*(1+r/n)^(n*t) = 100*(1+0.04/4)^(4*3) = $112.68

So, final value = $112.68

4). Amount borrowed PV = $5000

time period t = 3 years

rate r = 8%

So, amount owed now = PV*(1+r)^t = 5000*1.08^3 = $6298.56