Question

Claire Fitch is planning to begin an individual retirement program in which she will invest $1,500 at the end of each year. Fitch plans to retire after making 30 annual investments in the program earning a return of 10%. What is the value of the program on the date of the last payment (30 years from present)?

Answer 1

The value of the retirement program on the date of the last payment is approximately $196,608.04.

Step-by-step explanation:

To calculate the value of the retirement program, we can use the formula for calculating the future value of an annuity. The formula is:

FV = P * [(1 + r)²n - 1] / r

Where FV is the future value, P is the annual investment, r is the annual interest rate, and n is the number of years. In this case, P = $1,500, r = 10% (or 0.10), and n = 30. Plugging these values into the formula, we get:

FV = $1,500 * [(1 + 0.10)^30 - 1] / 0.10 = $196,608.04

Therefore, the value of the program on the date of the last payment is approximately $196,608.04.

Answer 2

$246,741.03

Step-by-step explanation:

This is an ordinary annuity(payments occur at the end of each year). The question is basically asking for it's future value. Using a financial calculator, input the following;

Total duration; N = 30

Interest rate; I/Y = 10%

Recurring payment; PMT = -1,500

One time payment ; PV = 0

then compute future value; CPT FV = 246,741.03

Therefore; the value of the program on the date of the last payment will be $246,741.03