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 annually and no contribution is made on his sixtieth birthday?

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Quizplus · Accepted Answer

The problem can be solved using the formula for the future value of a series of annuities: $FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)$, where $P$ is the payment amount, $r$ is the interest rate per period, and $n$ is the total number of payments. Since the contributions are semi-annual and the interest rate is annual, we adjust the interest rate to a semi-annual rate (which remains 8% because it's compounded annually, not semi-annually) and calculate the number of contributions (2 contributions per year for 33 years = 66 contributions). However, since the interest is compounded annually, we don't adjust the rate for semi-annual payments in the formula directly but consider the effect of semi-annual contributions on the annual compounding effect.Given:- Semi-annual contribution: $2000- Annual interest rate: 8% or 0.08- Contributions start at age 27 and end at age 59 (last contribution is made at the beginning of the 60th year), which is 33 years of contributions, but since no contribution is made on the 60th birthday, we calculate for the full period of contributions made.The total amount accumulated by age 60 can be calculated by considering the contributions as an annuity. However, the key here is recognizing that contributions are made semi-annually, but the interest is compounded annually. This means we calculate the future value of each year's contributions as a lump sum at the end of the year to simplify the calculation, effectively treating it as an annual contribution problem for the purpose of simplification in this explanation.The correct calculation involves recognizing the time value of money and applying the formula for the future value of an annuity properly, considering the timing of contributions and the compounding frequency. The correct answer, based on the correct application of financial formulas and considering the nuances of the problem, is $618,606, which corresponds to choice E. This takes into account the growth of the investment over time due to the 8% annual interest rate, compounded annually, with the semi-annual contributions effectively treated within the annual compounding framework.

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