Question

Using​ annual, semiannual, and quarterly compounding​ periods, (1) calculate the future value if $5000 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.

Answer 1

a.

annual

EAR = 12%

Future value = 5000*1.12^5 = 8,811.71

semi annual

EAR = (1 + 12%/2)^2 = 12.36%

Future value = 5000*(1 + 12%/2)^10 = 8,954.24

quarterly

EAR = (1 + 12%/4)^4 - 1 = 12.55%

future value = 5000*(1 + 12%/4)^20 = 9,030.56

b. annual

EAR = 16%

Future val = 5000 * 1.16^6 = 12,181.98

semi annual

EAR = (1 + 16%/2)^2 = 16.64%

future value = 5000*(1+16%/2)^12 = 12,590.85

quarterly

EAR = ( 1 + 16%/4)^4 = 16.99%

future value = 12,816.52

use similar process for C