A fund is started at $\$1000$ and compound interest is reckoned at $4\%$ per annum. If withdrawa

Question

A fund is started at $\$1000$ and compound interest is reckoned at $4\%$ per annum. If withdrawals of $\$50$ are made at the beginning of each of the subsequent years, show that the amount in the fund at the beginning of the ${(n+1)^{\mathrm{th}}}$ year is $\$$ $1250\left[1 - \frac{1}{5}(1.04)^n\right]$ Find the amount in the fund to the nearest dollar after twenty years, and also how many years it will last.

Accepted Answer

Fund at the beginning of year $n+1$: $1250\left[1-\frac15(1.04)^n\right]$. After $20$ years: $\$702$. Duration: $42$ years.

Compound Interest with regular writhdrawals

Compound Interest with regular writhdrawals

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