Cameron is 35 years old and intends to retire at the age of 60. He is planning to contribute $3000 at the beginning of each six-month period to an RRSP. What semi-annually compounded rate of interest must his RRSP earn in order to reach $600 000 after 25 years?

Question

Quizplus · Accepted Answer

Firstly, we need to find out the number of contributions Cameron will make:
$3000 every six months for 25 years = 50 years / 6 months = 100 contributions

Next, we need to calculate the future value of these contributions. We can use the formula:
FV = PMT * ((1 + r)^n - 1) / r

Where:
PMT = payment made every six months = $3000
r = semi-annual compound interest rate that we want to find
n = number of contributions = 100
FV = future value we want to achieve = $600,000

Substituting these values into the formula and solving for r gives us:
$600,000 = $3000 * ((1 + r)^100 - 1) / r
r ≈ 0.0473 (or 4.73%)

However, the question asks for the semi-annually compounded rate, so we need to divide this by 2:
4.73% / 2 = 2.365% per six-month period

Therefore, the closest answer choice is B) 9.43% (which is twice the semi-annual rate we calculated).

Cameron Is 35 Years Old and Intends to Retire at the Age