Question

Since the birth of his daughter, 19 years ago, Casey has deposited $75 at the beginn of every month into a Registered Education Savings Plan (RESP). The interest rate on the plan was 4.90% compounded monthly for the first 10 years and 4.50% compounded monthly for the next 9 years.

a. What would be the accumulated value of the RESP at the end of 10 years? Round to the nearest cent
b. What would be the accumulated value of the RESP at the end of 19 years? Round to the nearest cent

Answer 1

The accumulated value of the RESP at the end of 10 years is $12,978.67, and at the end of 19 years is $10,745.81.

Step-by-step explanation:

To calculate the accumulated value of the RESP at the end of 10 years, we can use the formula for compound interest: A = P(1+r/n)^(nt), where A is the accumulated value, P is the principal (initial deposit), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.
For the first 10 years, the interest rate is 4.90% compounded monthly, so r = 0.0490 and n = 12. The principal is $75, and the number of years is 10. Plugging in these values into the formula, we get: A = 75(1+0.0490/12)^(12*10) = $12,978.67.
To calculate the accumulated value at the end of 19 years, we follow the same process, but for the next 9 years, where the interest rate is 4.50%. Using the formula for compound interest, we get: A = 75(1+0.0450/12)^(12*9) = $10,745.81. Therefore, the accumulated value of the RESP at the end of 19 years would be $10,745.81.