(5 POINTS ) 22) Find the present value of an annuity of $$ \$ 100 $$ paid at the end of each year for 17 years if the interest rate is $$ 7 \% $$,

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To find the present value of an annuity, we can use the present value of annuity formula:

$$
PV = P \times \left( \frac{1 - (1 + r)^{-n}}{r} \right)
$$

Where:
- $$ PV $$ = Present Value of the annuity
- $$ P $$ = Payment amount per period
- $$ r $$ = Interest rate per period
- $$ n $$ = Total number of payments

In this case:
- $$ P = 100 $$
- $$ r = 0.07 $$ (7% as a decimal)
- $$ n = 17 $$

Now, we can plug in the values:

$$
PV = 100 \times \left( \frac{1 - (1 + 0.07)^{-17}}{0.07} \right)
$$

Calculating $$ (1 + 0.07)^{-17} $$:

$$
(1 + 0.07)^{-17} = (1.07)^{-17} \approx 0.2924
$$

Now substituting this back into the formula:

$$
PV = 100 \times \left( \frac{1 - 0.2924}{0.07} \right)
$$

Calculating $$ 1 - 0.2924 $$:

$$
1 - 0.2924 = 0.7076
$$

Now substituting this value:

$$
PV = 100 \times \left( \frac{0.7076}{0.07} \right)
$$

Calculating $$ \frac{0.7076}{0.07} $$:

$$
\frac{0.7076}{0.07} \approx 10.1071
$$

Finally, calculating the present value:

$$
PV = 100 \times 10.1071 \approx 1010.71
$$

Thus, the present value of the annuity is approximately:

$$
\boxed{1010.71}
$$
The present value of the annuity is approximately \$1010.71.

(5 POINTS ) 22) Find the present value of an annuity of \( \$ 100 \) paid at the end of each year for 17 years if the interest rate is \( 7 \% \),

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