Question

Changing compounding frequency Using annual, semiannual, and quarterly compounding periods, (1) calculate the future value if $6,000 is deposited initially at 11% annual interest for 7 years, and (2) determine the effective annual rate (EAR) Annual Compounding (1) The future value, Vn, is (Round to the nearest cent.) 2) If the 11% annual nominal rate is compounded annually the EAR is 96 Round to two decimal places Semiannual Compounding (1) The future value, Vn, is (Round to the nearest cent.) (2 if the 11% annual nominal rate is compounded semiannually, the EAR is 96 Round to two decimal places. Quarterly Compounding (1) The future value, Vn, is (Round to the nearest cent.) 2) If the 11% annual nominal rate is compounded quarterly, the EAR is 96 Round to two decimal places Round to two decimal places.)

Answer 1

Answer A (1) and A (2):

Deposit = $6,000

Annual interest rate = 11%

Period = 7 years

FV = $6,000 * (1 + 11%) ⁷

= $12,456.96

When annual rate is compounded annually, the EAR will remain same as annual rate = 11.00%

Answer B(1) and B(2):

Compounded semiannually:

Semiannual rate of interest = 11%/2 =5 .5%

Number of semiannual periods = 7 * 2 = 14

FV = $6,000 * (1 + 5.5%) ¹⁴

= $12,696.55

EAR = (1 + Nominal Interest rate / Number of compounding periods) ^{Number of compounding periods} - 1

= (1 + 11%/2) ²  - 1

=11.30%

Answer C(1) and C(2):

Compounded quarterly:

Quarterly rate of interest = 11%/4 =2.75%

Number of quarterly periods = 7 * 4 = 28

FV = $6,000 * (1 + 2.75%) ²⁸

= $12,824.56

EAR = (1 + Nominal Interest rate / Number of compounding periods) ^{Number of compounding periods} - 1

= (1 + 11%/4) ⁴ - 1

=11.46%