Question

OA-9 Close Date: Sun, Jul 3, 2022, 11:59 PM Question 4 of 4 Since the birth of her granddaughter, 16 years ago, Juan has deposited $250 at the beginning of every month into a Registered Education Savings Plan (RESP). The interest rate on the plan was 4. 50% compounded monthly for the first 9 years and 5. 00% compounded monthly for the next 7 years. A. What was the accumulated value of the RESP at the end of 9 years? b. What was the accumulated value of the RESP at the end of 16 years? $72,457. 88 Round to the nearest cent c. What was the amount of interest earned over the 16-year period? $24,457. 88 Round to the nearest cent

Answer 1

To calculate the accumulated value of the RESP at different time periods and the amount of interest earned, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A is the accumulated value
P is the principal amount (monthly deposit)
r is the interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years

Given the information provided, let's calculate each part:

(a) Accumulated value at the end of 9 years:
P = $250 (monthly deposit)
r = 4.50% or 0.045 (compounded monthly for 9 years)
n = 12 (monthly compounding)
t = 9

Using the formula:
A = 250(1 + 0.045/12)^(12*9) ≈ $44,063.76

(b) Accumulated value at the end of 16 years:
For the first 9 years, the interest rate is 4.50% compounded monthly.
For the next 7 years, the interest rate is 5.00% compounded monthly.

P = $250 (monthly deposit)

For the first 9 years:
r = 4.50% or 0.045 (compounded monthly)
n = 12 (monthly compounding)
t = 9

Using the formula:
A1 = 250(1 + 0.045/12)^(12*9)

For the remaining 7 years:
r = 5.00% or 0.05 (compounded monthly)
n = 12 (monthly compounding)
t = 7

Using the formula:
A2 = A1(1 + 0.05/12)^(12*7)

Calculating A2 will give us the accumulated value at the end of 16 years.

(c) Amount of interest earned over the 16-year period:
Interest earned = Accumulated value at the end of 16 years - Total deposits

Total deposits = Monthly deposit amount x Number of months (16 years x 12 months/year)

Let's calculate:

Total deposits = $250 x (16 x 12) = $48,000

Interest earned = Accumulated value at the end of 16 years - Total deposits

Now, using the values we calculated in (b) and (c), we can find the solution:

Accumulated value at the end of 16 years = A2

Interest earned over the 16-year period = A2 - $48,000

Round the results to the nearest cent.

Therefore:
(a) The accumulated value at the end of 9 years is approximately $44,063.76.
(b) The accumulated value at the end of 16 years is approximately $72,457.88.
(c) The amount of interest earned over the 16-year period is approximately $24,457.88.