Question

10)

1. FV of $800 paid each 6 months for 5 years at a nominal rate of 7% compounded semiannually. Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

2. FV of $400 paid each 3 months for 5 years at a nominal rate of 7% compounded quarterly. Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

3. These annuities receive the same amount of cash during the 5-year period and earn interest at the same nominal rate, yet the annuity in part b ends up larger than the one in part a. Why does this occur?
   -Select- The nominal deposits into the annuity in part (b) are greater than the nominal deposits into the annuity in part (a). The annuity in part (a) is compounded less frequently; therefore, more interest is earned on previously-earned interest. The annuity in part (a) is compounded more frequently; therefore, more interest is earned on previously-earned interest. The annuity in part (b) is compounded less frequently; therefore, more interest is earned on previously-earned interest. The annuity in part (b) is compounded more frequently; therefore, more interest is earned on previously-earned interest.

Answer 1

a)

payment made every 6 months = $800

Investment period = 5 years = 10 semi-annual periods

number of payments, n = 10

Nominal Annual Interest Rate = 7%

Nominal Semi-Annual Interest rate = Nominal Annual Interest Rate /2 = 7% /2 =3.5%

Future value of annuity is given by the formula

Where C = payment made each period = $800

i = semi-annual interest rate = 3.5%

n = number of payments = 10

FV = 800*11.73139316 = $9,385.11

b)

payment made every 3 months = $400

Investment period = 5 years = 20 quarterly periods

number of payments, n = 20

Nominal Annual Interest Rate = 7%

Nominal Quarterly Interest rate = Nominal Annual Interest Rate /4 = 7% /4 = 1.75%

Future value of annuity is given by the formula

Where C = payment made each period = $400

i = quarterly interest rate = 1.75%

n = number of payments = 20

FV = 400*23.70161119 = $9,480.64

c)

Annuity in part b ends up larger than the annuity in part a because the annuity in part b is compounded more frequently and therefore more interest is earned on previously earned interest

Hence Option no. 5 is correct

Option 1 is incorrect because the total nominal payments are the same

Option 2 is incorrect because less frequent compounding means less interest is earned

Option 3 is incorrect because annuity in part a is compounded less frequently

Option 4 is incorrect because annuity in part b is compounded more frequently