Questions: How much money must you pay into an account at the end of each of 20 years in order to have 10,000 at the end of the 20th year if the account pays 8% per annum, and you round to the nearest 1? Select one: a. 202 b. 184 c. 219 d. 225

Solution Steps

To solve this problem, we need to calculate the annuity payment required to reach a future value of $10,000 after 20 years with an annual interest rate of 8%. This involves using the future value of an annuity formula, which relates the future value, periodic payment, interest rate, and number of periods. We will rearrange the formula to solve for the periodic payment.

To find the annuity payment \( P \) required to accumulate a future value \( FV \) of \( 10,000 \) after \( n = 20 \) years at an interest rate \( r = 0.08 \), we use the future value of an annuity formula:

\[ FV = P \cdot \frac{(1 + r)^n - 1}{r} \]

Rearranging the formula to solve for \( P \):

\[ P = FV \cdot \frac{r}{(1 + r)^n - 1} \]

Substituting the known values into the formula:

\[ P = 10000 \cdot \frac{0.08}{(1 + 0.08)^{20} - 1} \]

Calculating \( (1 + 0.08)^{20} \):

\[ (1.08)^{20} \approx 4.660 \]

Thus, we have:

\[ P = 10000 \cdot \frac{0.08}{4.660 - 1} = 10000 \cdot \frac{0.08}{3.660} \approx 218.522 \]

Rounding \( P \) to the nearest dollar gives:

\[ P \approx 219 \]

Final Answer