Money for the future

Algebra Level 3

At the end of each six months for eight years, a man deposits $ 500 \$500 in a fund to provide for the education of his son. If the fund accumulates at the rate 4 % 4\% compounded semi-annually, how much is in the fund (in $ \$ ) just after the 1 1 t h 11^{th} deposit? Give your answer to the nearest integer.


The answer is 6084.

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1 solution

We can use the formula: F = A [ ( 1 + i ) n − 1 ] i F=\dfrac{A[(1+i)^n-1]}{i} where: F F is the future worth, A A is the annuity, n n is the total number of compundings, and i i is the effective interest per compunding period (per interst period)

F = 500 [ ( 1 + 0.04 2 ) ( 5.5 ) ( 2 ) − 1 ] 0.04 2 ≈ 6084 F=\dfrac{500\left[\left(1+\dfrac{0.04}{2}\right)^{(5.5)(2)}-1\right]}{\dfrac{0.04}{2}}\approx 6084

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