## Question

###### If $P$ dollars are invested annually in an annuity (investment fund), after $n$ years, the annuity will be worth $$W=P\left[\frac{(1+i)^{n}-1}{i}\right]$$ where i is the interest rate, compounded annually. Suppose that you establish an annuity that earns $7 \frac{1}{4} \%$ interest, and you want it to be worth $\$ 50,000$ in 20 yr. How much will you need to invest annually to achieve this goal?

If $P$ dollars are invested annually in an annuity (investment fund), after $n$ years, the annuity will be worth $$W=P\left[\frac{(1+i)^{n}-1}{i}\right]$$ where i is the interest rate, compounded annually. Suppose that you establish an annuity that earns $7 \frac{1}{4} \%$ interest, and you want it to be worth $\$ 50,000$ in 20 yr. How much will you need to invest annually to achieve this goal?

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