Jawad makes semi-annual contributions of $2000 starting on his 27th birthday. How much will he accumulate in his RRSP by age 60, if RRSP earns 8% compounded semi-annually and no contribution is made on his sixtieth birthday?

Question

Quizplus · Accepted Answer

To calculate the future value of Jawad's RRSP, we use the future value of an annuity formula, considering semi-annual contributions and compounding. The formula is $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $P$ is the payment amount per period, $r$ is the interest rate per period, and $n$ is the total number of payments.Given:- $P = \$2000$- Annual interest rate = 8% or 0.08, so the semi-annual rate $r = 0.08/2 = 0.04$ (since interest is compounded semi-annually)- Jawad contributes from age 27 to just before his 60th birthday, so for 33 years. Since contributions are semi-annual, $n = 33 \times 2 = 66$ periods.Plugging these values into the formula:$$FV = \$2000 \times \frac{(1 + 0.04)^{66} - 1}{0.04}$$$$FV = \$2000 \times \frac{(1.04)^{66} - 1}{0.04}$$$$FV = \$2000 \times 320.078$$$$FV = \$640,156$$Therefore, by age 60, Jawad will have accumulated \$640,156 in his RRSP.

Jawad Makes Semi-Annual Contributions of $2000 Starting on His 27th