Question

Suppose a person has contributed $2,000 per year for 30 years at 6% interest rate and then retired. The balance in the account is then used to purchase an annuity which will make a payment at the end of each month for the following 20 years, completely exhausting the account. The annuity pays 7.29% compounded monthly. What will the amount of the monthly payment be?

PLEASE SHOW WORK

Answer 1

Firstly, the balance in the account at the end of 30 years is calculated.

The balance in the account at the end of 30 years is calculated by computing the future value

Yearly payment= $2,000

Interest rate= 6%

Time= 30 years

The future value of the annuity is calculated by entering the below:

PMT= 2,000; I/Y= 6; N= 30

Press CPT and FV to calculate the future value.

The balance in the account at the end of 30 years is $158,116.37.

Secondly, the monthly payment of the annuity purchased should be calculated.

Present value= $158,116.37

Interet rate= 7.29%/12= 0.6075%

Time= 20 years*12= 240 months

The monthly payment is calculated by entering the below:

PV= -158,116.37; N= 240; I/Y= 0.6075

Press CPT and PMT to calculate the monthly payment.

The monthly payment is $1,253.55.