Question

Carl is the beneficiary of a $21,000 trust fund set up for him by his grandparents. Under the terms of the trust, he is to receive the money over a 6-year period in equal installments at the end of each year. If the fund earns interest at the rate of 2% year compounded annually, what amount will he receive each year? (Round your answer to the nearest cent.)

Answer 1

To determine Carl's annual payment from his trust, we use the present value annuity formula adjusted for a compound interest rate of 2% per year over 6 years. After calculations, Carl will receive approximately $3,749.88 per year.

Step-by-step explanation:

Carl needs to determine the amount of money he will receive each year from a $21,000 trust fund that is to be paid out in equal installments over 6 years, with an interest rate of 2% compounded annually. To calculate this, we can use the formula for the annuity payment given a present value, which considers the compound interest rate:

The formula is PV = PMT × [(1 - (1 + r)^{-n}) / r], where PV is the present value of the trust fund, PMT is the payment each period, r is the interest rate per period, and n is the number of periods.

Rearranging the formula to solve for PMT gives us:
PMT = PV / [(1 - (1 + r)^{-n}) / r]

Plugging in the values:
PMT = $21,000 / [(1 - (1 + 0.02)^{-6}) / 0.02] → PMT = $21,000 / 5.6014

Now by calculating it we get:

PMT = $3,749.88

Therefore, Carl will receive approximately $3,749.88 at the end of each year for 6 years.