Questions: a. Use the appropriate formula to find the value of the annuity. b. Find the interest. Periodic Deposit Rate Time 1000 at the end of each year 6.5% compounded annually 20 years (i) Click the icon to view some finance formulas. a. The value of the annuity is . (Do not round until the final answer. Then round to the nearest dollar as needed.) b. The interest is . (Use the answer from part (a) to find this answer. Round to the nearest dollar as needed.)

Solution Steps

To calculate the future value of an annuity, we use the formula: $$FVA = PMT \times \left(\frac{(1 + \frac{r}{n})^{n \times t} - 1}{\frac{r}{n}}\right)$$ Substituting the given values: $PMT = 1000$, $r = 0.065$, $n = 1$, and $t = 20$, we get: $$FVA = 1000 \times \left(\frac{(1 + \frac{0.065}{1})^{20} - 1}{\frac{0.065}{1}}\right) = 38825$$

The total amount of deposits is calculated as: $Total Deposits = PMT \times n \times t = 20000$. Thus, the total interest earned is: $Total Interest = FVA - Total Deposits = 38825 - 20000 = 18825$.

Final Answer