Question

Mrs. Riin Rivanool set up a trust fund today for her great-granddaughters education that would help with her education in 17 years from today. If she deposits $150 at the end of every month for those 17 years into a trust earning 6% compounded quarterly, determine: ( 6 marks) (a) How much money is there in 17 years from today? (b) What beginning of the quarter payment can be made for 5 years (afler the original 17 years) from the same 6% compound quarterly trust fund, before it nuss our?

Answer 1

The amount of money in the trust fund after 17 years is approximately $6,586.21. The beginning of the quarter payment that can be made for 5 years after the original 17 years is approximately $4,746.54.

Step-by-step explanation:

To determine how much money will be in the trust fund in 17 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future value, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

(a) In this case, the principal amount is $150, the interest rate is 6% (or 0.06), and interest is compounded quarterly (n = 4). We want to find A, so we substitute the given values into the formula: A = 150(1 + 0.06/4)^(4*17). Calculating this, we find that there will be approximately $6,586.21 in the trust fund after 17 years.

(b) To determine the beginning of the quarter payment that can be made for 5 years after the original 17 years, we can use the same formula. However, in this case, we will only be compounding interest for 5 years, so t = 5. We want to find the principal amount, P, so we can rearrange the formula: P = A / (1 + r/n)^(nt). Substituting the given values (A = $6,586.21, r = 0.06, n = 4, and t = 5), we find that the beginning of the quarter payment can be approximately $4,746.54.