Question

Compound interest with nonannual periods​)

a. Calculate the future sum of ​$5000​, given that it will be held in the bank for 5 years at an APR of 6 percent.

b. Recalculate part a using compounding periods that are​ (1) semiannual and​ (2) bimonthly​ (every two​ months).

c. Recalculate parts a and b for an APR of 12 percent.

d. Recalculate part a using a time horizon of 12 years​ (the APR is still 6 ​percent).

e. With respect to the effect of changes in the stated interest rate and holding periods on future sums in parts c and d​, what conclusions do you draw when you compare these figures with the answers found in parts a and b​?

a. What is the future sum of ​$5000 in a bank account for 5 years at an APR of 6 ​percent?

( ) (round to the nearest cent)

Answer 1

(a) Present Value = PV = $5000

Number of Periods = n = 5 years

Interest Rate = r = 6%

Hence, FV = PV(1+r)ⁿ = 5000(1+0.06)⁵ = $6691.13

(b)

(1)

Present Value = PV = $5000

Number of Periods = n = 5*2 = 10 semiannual periods

Interest rate = r = 6/2% = 3%

Hence, FV = PV(1+r)ⁿ = 5000(1+0.03)¹⁰ = $6719.58

(2)

Present Value = PV = $5000

Number of Periods = n = 5*6 = 30 bimonthly periods

Interest rate = r = 6/6% = 1%

Hence, FV = PV(1+r)ⁿ = 5000(1+0.01)³⁰ = $6739.24

(c)

Interest Rate = r = 12%

Hence, FV = PV(1+r)ⁿ = 5000(1+0.12)⁵ = $8811.71

(1) Number of Periods = n = 5*2 = 10 semiannual periods

Interest rate = r = 12/2% = 6%

Hence, FV = PV(1+r)ⁿ = 5000(1+0.06)¹⁰ = $8954.24

(2) Number of Periods = n = 5*6 = 30 bimonthly periods

Interest rate = r = 12/6% = 2%

Hence, FV = PV(1+r)ⁿ = 5000(1+0.02)³⁰ = $9056.81

(d) Present Value = PV = $5000

Number of Periods = n = 12 years

Interest Rate = r = 6%

Hence, FV = PV(1+r)ⁿ = 5000(1+0.06)¹² = $10060.98

(e) We can see from parts b that when the compounding frequency is increased, the future value increase. Part c indicates that increasing the rate of return increased the future value of the amount. Part d indicates that increasing the number of years also increases the future value of the amount.