Using annual, semiannual, and quarterly compounding periods for each of the following, (1) calculate the future value if $5,000 is deposited initially, and (2) determine the effective annual rate...

Using annual, semiannual, and quarterly compounding periods for each of the following, (1) calculate
the future value if $5,000 is deposited initially, and (2) determine the effective annual rate (EAR).
a. At 12% annual interest for 5 years.
b. At 16% annual interest for 6 years.
c. At 20% annual interest for 10 years.
Solution:
Initial investment, A = $5,000
EAR = (1+r/p)^p - 1
Future value of Investment, FV = A*(1+r)^n
a. At 12% annual interest for 5 years
Annual compounding:
Interest rate, R = 12%
Compounding = Annual
No of periods in a year, p = 1
Periodic interest rate, r = 12% / 1 = 12%
No. of years = 5
Total period, n = 1*5 = 5
EAR = [(1+12%/1)^1] – 1 = 12%
Future value of Investment, FV = 5,000*(1+12%)^5 = $8,811.71
Semi-annual compounding:
Interest rate, R = 12%
Compounding = Semi-annual
No of periods in a year, p = 2
Periodic interest rate, r = 12% / 2 = 6%
No. of years = 5
Total period, n = 2*5 = 10
EAR =...