Question

​(Related to Checkpoint​ 5.2)  

​(Compoundinterest with​ non-annual periods​)

You just received a bonus of ​$5,000.

a.  Calculate the future value of ​$5,000​, 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 12 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]

future value = present value * (1 + r)^t

where r = annual rate of interest

t = number of years

future value = $5,000 * (1 + 6%)⁵ = $6,691.13

b]

1]

future value = present value * (1 + (r/n))^nt

where r = annual rate of interest

n = number of compounding periods per year

t = number of years

future value = $5,000 * (1 + (6%/2))^2*5 = $6,719.58

2]

future value = present value * (1 + (r/n))^nt

where r = annual rate of interest

n = number of compounding periods per year

t = number of years

future value = $5,000 * (1 + (6%/6))^6*5 = $6,739.24

c]

a]

future value = present value * (1 + r)^t

where r = annual rate of interest

t = number of years

future value = $5,000 * (1 + 12%)⁵ = $8,811.71

b]

1]

future value = present value * (1 + (r/n))^nt

where r = annual rate of interest

n = number of compounding periods per year

t = number of years ,

future value = $5,000 * (1 + (12%/2))^2*5 = $8,954.24

2]

future value = present value * (1 + (r/n))^nt

where r = annual rate of interest

n = number of compounding periods per year

t = number of years

future value = $5,000 * (1 + (12%/6))^6*5 = $9,056.81

d]

future value = present value * (1 + r)^t

where r = annual rate of interest

t = number of years

future value = $5,000 * (1 + 6%)¹² = $10,060.98