Gerry make quarterly deposits $2,000 at the end of every 3-month period in a fund earning interest compounded semi-annually at j₂ = 8%.If the fund pays simple interest for the fractional part of any interest period,what is the accumulated value of Gerry's deposits at the end of 5 years?

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Quizplus · Accepted Answer

The accumulated value of Gerry's deposits can be calculated using the formula for the future value of a series of payments, considering the semi-annual compounding for full periods and simple interest for the fractional part. Given the interest rate is 8% compounded semi-annually, the nominal rate is 4% per semi-annual period. Gerry makes quarterly deposits, so we need to account for the interest compounding and the simple interest for the fractional part of the year.For a 5-year period, Gerry will make 20 deposits (5 years * 4 quarters). The last deposit will not earn any interest, and the first deposit will earn interest for 20 quarters.The future value of an annuity formula for compounded interest is $FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)$, where $P$ is the payment amount, $r$ is the interest rate per period, and $n$ is the number of periods.However, since the interest is compounded semi-annually, we need to adjust our calculations for the deposits that do not align with the compounding period. The deposits will earn simple interest for the fractional part of the semi-annual period.Given the complexity of the calculation due to the mix of compounding and simple interest, and without going into the detailed step-by-step calculation, we can use financial calculators or spreadsheet software to compute the future value considering the specific conditions.The correct answer, considering the semi-annual compounding and the simple interest for the fractional part, is approximately $48,504.67, which matches option D. This calculation takes into account the effect of compounding as well as the simple interest for the periods that do not fully align with the semi-annual compounding periods.

Gerry Make Quarterly Deposits $2,000 at the End of Every