Question

Brett invested $1,800 at the beginning of every 6 months in an RRSP for 11 years. For the first 8 years it earned interest at a rate of 3.70% compounded semi-annually and for the next 3 years it earned

interest at a rate of 5.80% compounded semi-annually.
a. Calculate the accumulated value of her investment at the end of the first 8 years.
$51,710.11
$52,046.92
$33,162.68
$33,776.19

b. Calculate the accumulated value of her investment at the end of 11 years.
$51,710.11
$52,046.92
$45,726.94
$33,776.19

c. Calculate the amount of interest earned from the investment.
$12,446.92
$12,110.11
$11,296.17
$1,150.75

Answer 1

To solve the problem, we must calculate the future value of the investments at 3.70% for first 8 years, then at 5.80% for next 3 years using the annuity formula. The amount of interest earned is the final accumulated value minus the total amount invested.

Step-by-step explanation:

We need to calculate the future value of a series of periodic investments using the formula for compound interest. Since there are two different interest rates involved, we will break the calculation into two parts: the first 8 years at 3.70% compounded semi-annually, and the next 3 years at 5.80% compounded semi-annually.

For the first 8 years, Brett invests $1,800 every 6 months. We will use the future value of an annuity formula for this part:

`FV = P × { [ (1 + r)^(n) - 1 ] / r }`

Where:

• P is the periodic payment ($1,800)
• r is the interest rate per period (3.70% / 2 = 0.0185)
• n is the total number of payments (8 years × 2 periods per year = 16)

Calculating it, we'll find the value at the end of 8 years.

For the remaining 3 years, we need to calculate the compound interest on the accumulated sum of the first 8 years, additionally investing $1,800 every 6 months at the new rate (5.80% / 2 = 0.029), and calculate the new future value.

Finally, to find the total amount of interest earned, we subtract the total amount of investments from the final accumulated value. Since the total amount of investments is $1,800 every 6 months for 11 years, it is $1,800 × 22 periods.