Question

You just received a bonus of ​$3,000.

a.  Calculate the future value of ​$3 comma 000​, given that it will be held in the bank for 5 years and earn an annual interest rate of 6 percent.

b.  Recalculate part ​(a​) using a compounding period that is​ (1) semiannual and​ (2) bimonthly.

c.  Recalculate parts ​(a​) and ​(b​) using an annual interest rate of 12 percent.

d.  Recalculate part ​(a​) using a time horizon of 10 years at an annual interest rate of 6 percent.

e.  What conclusions can you draw when you compare the answers in parts ​(c​) and ​(d​) with the answers in parts ​(a​) and ​(b​)?

Answer 1

(a) Present Value = PV = $3000

Number of periods = n = 5 years

Interest Rate = r = 6%

Future Value = FV = PV(1+r)ⁿ = 3000(1+0.06)⁵ = 4014.68

(b)

1. Present Value = PV = $3000

Number of periods = n = 10 semiannual periods

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

Future Value = FV = PV(1+r)ⁿ = 3000(1+0.03)¹⁰ = 4031.74

2. Present Value = PV = $3000

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

Interest Rate = r = 6%/6 = 1%

Future Value = FV = PV(1+r)ⁿ = 3000(1+0.01)³⁰ = 4043.55

(c)

1.

Present Value = PV = $3000

Number of periods = n = 5 years

Interest Rate = r = 12%

Future Value = FV = PV(1+r)ⁿ = 3000(1+0.12)⁵ = 5287.03

2. Present Value = PV = $3000

Number of periods = n = 10 semiannual periods

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

Future Value = FV = PV(1+r)ⁿ = 3000(1+0.06)¹⁰ = 5372.54

2. Present Value = PV = $3000

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

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

Future Value = FV = PV(1+r)ⁿ = 3000(1+0.02)³⁰ = 5434.08

(d)

Present Value = PV = $3000

Number of periods = n = 10 years

Interest Rate = r = 6%

Future Value = FV = PV(1+r)ⁿ = 3000(1+0.06)¹⁰ = 5372.54

(e) We can observe in parts c and d that as the interest rate increases, the future value of the investment increases. As the number of years to maturity increases, future value increases