Final answer:
To find out Mr. Smith's total amount in his RRSP after 15 years, we need to apply the future value of an annuity formula considering the contributions, interest rate, and compounding periods. The formula takes into account the effect of compound interest, which is significant over long periods and with regular contributions. Once we determine the equivalent quarterly interest rate and adjust the number of compounding periods, the formula will reveal the total amount.
Step-by-step explanation:
To calculate how much Mr. Smith will have in his RRSP after 15 years, we must use the formula for future value of an annuity with compound interest. Compounded interest means that at each compounding period, interest is added to the principal, and then the next interest calculation is based on the total of the principal plus the previously accumulated interest.
The formula for the future value of an annuity compounded at different periods than the payment periods is as follows:
PV = Principal Value (initial amount)PMT = Payment amount per periodr = Interest rate per periodn = Total number of compounding periodst = Total number of payments
In Mr. Smith's case, his contributions can be considered as an annuity since he contributes a fixed amount regularly. Given the interest rate is 5% per annum compounded quarterly, and he makes contributions biannually, we can calculate the equivalent quarterly interest rate and adjust the number of compounding periods accordingly. After these calculations, we can then apply the future value of an annuity formula to determine the total value of the RRSP after 15 years.