Question

At age 25, Alan starts paying $2000 each year into an investment fund. He is guaranteed a 4% interest rate throughout the savings period. How much will he have in the investment fund at the end of 30 years? Note for this particular pension the payments are made at the beginning of each year, and the interest is paid at the end of each year.

a) $102,565.68
b) $99,450.32
c) $100,000.00
d) $105,126.74

Answer 1

Alan will have $99,450.32 in his investment fund at the end of 30 years, using the future value of an annuity due formula for calculations.

Step-by-step explanation:

To calculate how much Alan will have in the investment fund at the end of 30 years, we need to use the formula for the future value of an annuity due, which accounts for payments made at the beginning of each period.

For an annuity due, the future value can be calculated using the formula:
FV = P × ((1 + r)n - 1) × (1 + r) / r

Where:
• P is the annual payment
• r is the annual interest rate
• n is the number of periods

In Alan's case, he makes an annual payment P of $2,000, the annual interest rate r is 4% or 0.04, and the number of years n is 30.

Substituting these values into the formula, we get:
• FV = 2000 × ((1 + 0.04)30 - 1) × (1 + 0.04) / 0.04

Calculating the above expression, we get the future value of Alan's investment, which is answer choice (b) $99,450.32.