Question

Question Mode
Multiple Choice Question
Calculate the present value of a 10-year, 6% loan with annual payments of $7,500 made at the end of each year. (Use the tables in the Appendix to calculate your answer.)

Multiple choice question.

$32,663


$70,725


$55,200


$75,000

Answer 1

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

\[
PV = P \times \left(1 - (1 + r)^{-n}\right) / r
\]

Where:
- \( PV \) = present value of the annuity
- \( P \) = payment amount ($7,500)
- \( r \) = interest rate (6% or 0.06)
- \( n \) = number of periods (10 years)

Let's plug in the values:

1. \( P = 7500 \)
2. \( r = 0.06 \)
3. \( n = 10 \)

Now we calculate:

\[
PV = 7500 \times \left(1 - (1 + 0.06)^{-10}\right) / 0.06
\]

First, calculate \( (1 + 0.06)^{-10} \):

\[
(1 + 0.06)^{-10} = (1.06)^{-10} \approx 0.558394
\]

Now substitute back:

\[
PV = 7500 \times \left(1 - 0.558394\right) / 0.06
\]
\[
PV = 7500 \times (0.441606) / 0.06
\]
\[
PV = 7500 \times 7.360099
\]
\[
PV \approx 55200.74
\]

Rounding to the nearest dollar gives us approximately $55,201.

Therefore, the closest answer from your options is:

**$55,200**.