Question

Harry paid ​$250000 for a​ fifteen-year indexed annuity in which the monthly payments received at the end of each month increase by​ 0.7% per payment. What is the total amount received by Harry if interest is​ 8.4% compounded​ monthly?

Answer 1

If interest is 8.4% compounded monthly, the total amount received by Harry is $317,985.20.

Present value = $250,000

Years of investment = 15 years

To solve this problem, we need to use the formula for the future value of an annuity:

`FV = PMT [(1 + r)^n - 1]/r`

Where:

FV = the future value

PMT = the monthly payment

r = the monthly interest rate

n = the number of payments.

From the annual interest rate, we need to compute the monthly interest rate:

r = 8.4%/12 = 0.7%

n = 180 months (15 x 12)

The monthly payment using the present value of the annuity with PV = $250,000:

`PMT = PV / [(1 - (1 + r)^(-n))/r]`

PMT = $250000 / [(1 - (1 + 0.7%)^-180)/0.7%]

PMT = $1,766.59

The total amount received by Harry is the product of the monthly payment by the number of payments:

Total amount received = PMT x n

Total amount received = $1,766.59 x 180

Total amount received = $317,985.20

Thus, we can conclude that the total amount received by Harry is $317,985.20.