You initially deposit $25,000 and contribute $250 per quarter for the next 10 years. If the rate of interest is 4% compounded quarterly, calculate the future value.

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Quizplus · Accepted Answer

The future value of an investment can be calculated using the formula for the future value of an annuity and adding it to the future value of a lump sum. The future value of the lump sum (initial deposit) is calculated using the formula $FV = PV(1 + r)^n$, where $PV$ is the present value, $r$ is the interest rate per period, and $n$ is the number of periods. The future value of the annuity (quarterly contributions) is calculated using the formula $FV_{\text{annuity}} = P\frac{(1 + r)^n - 1}{r}$, where $P$ is the payment per period, $r$ is the interest rate per period, and $n$ is the number of periods.Given:- Initial deposit ($PV$) = $25,000- Quarterly contribution ($P$) = $250- Annual interest rate = 4% or 0.04- Interest rate per quarter = $0.04 / 4 = 0.01$ or 1%- Number of years = 10- Number of quarters ($n$) = $10 \times 4 = 40$First, calculate the future value of the initial deposit:$$FV_{\text{lump sum}} = 25000(1 + 0.01)^{40}$$Then, calculate the future value of the quarterly contributions:$$FV_{\text{annuity}} = 250\frac{(1 + 0.01)^{40} - 1}{0.01}$$Adding both values gives the total future value of the investment. When you perform these calculations, you should find that the total future value closely matches option A, $49,443. This accounts for both the compounded interest on the initial deposit and the compounded interest on the quarterly contributions.

You Initially Deposit $25,000 and Contribute $250 Per Quarter for the Next