Using annual, semiannual, and quarterly compounding periods for each of the following, (1) calculate...

Question

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.

David · Accepted Answer

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,

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...

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