An annuity pays $100 at the end of each quarter for ten years. The payments are

ID: 2725684 • Letter: A

Question

An annuity pays $100 at the end of each quarter for ten years. The payments are made directl to a savings account with a nominal interest rate of 4.85% payable monthly, and they are left in the account a) find the effective interest rate for a quarter and use it to compute the balance in the savings account immediately after the last payment An annuity pays $100 at the end of each quarter for ten years. The payments are made directl to a savings account with a nominal interest rate of 4.85% payable monthly, and they are left in the account a) find the effective interest rate for a quarter and use it to compute the balance in the savings account immediately after the last payment a) find the effective interest rate for a quarter and use it to compute the balance in the savings account immediately after the last payment

Explanation / Answer

Calculation of Effective rate of return for a quarter:

Nominal Yearly rate =

4.85%

Nominal Monthly rate = 4.85%/12 =

0.40%

Effective rate of return for a quarter = (1+0.40%)^3 - 1 =

1.20481%

Calculation of balance In the saving account at the end:

Amount of Quarterly Payments

$100

Number of Quarterly Payments = (10 Years *4) =

Quarterly Rate of Interest

1.20481%

Future value of annuity (1.20481%, 40 Periods) =

51.00636

Balance In the saving account at the end = $100*51.00636 =

$ 5,100.64