Question

a. Use the appropriate formula to find the value of the annuityb. Find the interest.Periodic Deposit$4000 at the end of each yearRate5% compounded annuallyTime10 yearsa. The value of the annuity is $(Do not round until the final answer. Then round to the nearest dollar as needed.)

Answer 1

We have a deposit of $4000 at the end of each year.

The rate is 5% compounded annually (r = 0.05).

The number of periods is n = 10.

We have to calculate the present value of the annuity.

We will use the formula:

$PV=C\cdot\frac{1-(1+r)^{-n}}{i}$

If we replace with our data, we get:

$\begin{gathered} PV=4000\cdot\frac{1-(1+0.05)^{-10}}{0.05} \\ PV=4000\cdot\frac{1-1.05^{-10}}{0.05} \\ PV=4000\cdot\frac{1-\frac{1}{1.05^{10}}}{0.05} \\ PV=4000\cdot7.72173492918481251283 \\ PV\approx30887 \end{gathered}$

Now, we have to calculate the interest.