Question

A trust fund for a 12-year-old child is being set up by a single payment so that at the age 21 the child will receive $20,000. Find how much the payment is if an interest rate of 9% compounded semiannually is assumed.

Answer 1

To determine the initial investment for the trust fund, we apply the compound interest formula, calculating the principal amount necessary to grow to $20,000 in 9 years at a 9% annual interest rate, compounded semiannually.

Step-by-step explanation:

The subject of this question is Mathematics, and it is suitable for a High School grade level. The question deals with finding the initial payment required to set up a trust fund that will grow to a certain future value with compound interest. To solve this, we use the compound interest formula, which is P = A / (1 + r/n)nt, where P is the principal amount (initial payment), A is the future value, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

To calculate the initial payment for the trust fund accruing a 9% interest rate compounded semiannually over 9 years until the child turns 21 to amount to $20,000, we can set up the equation as follows: P = 20,000 / (1 + 0.09/2)(2*9). Simplifying this, we find the amount needed to deposit initially.