Question

harley took out a 1 year loan for $2800 at an electronics store to be paid back with monthly payments at a 16.8% APR, compounded monthly. if the loan offers no payments for the first 3 months, how much will harley owe when he begins making payments?

A. $3308.37
B. $2800.00
C. $3173.22
D. $2919.25

Answer 1

To find out how much Harley will owe after the initial 3-month period with no payments, we need to calculate the compounded amount of the loan after 3 months.

The formula for compound interest is given by:

\[
A = P(1 + r/n)^{nt}
\]

Where:
- \( A \) = the amount of money accumulated after n years, including interest.
- \( P \) = the principal amount (the initial amount of money).
- \( r \) = annual interest rate (decimal).
- \( n \) = number of times that interest is compounded per year.
- \( t \) = the time the money is invested or borrowed for, in years.

In this case:
- \( P = \$2800 \)
- \( r = 16.8\% = 0.168 \)
- \( n = 12 \) (since the interest is compounded monthly)
- \( t = 3/12 \) (3 months out of 12 months)

Now we can substitute these values into the formula:

\[
A = 2800 \left(1 + \frac{0.168}{12}\right)^{12 \cdot \frac{3}{12}}
\]

Calculating it step by step:

1. Calculate \( \frac{0.168}{12} \):

\[
\frac{0.168}{12} = 0.014
\]

2. Now add 1 to this value:

\[
1 + 0.014 = 1.014
\]

3. Calculate the exponent:

\[
12 \cdot \frac{3}{12} = 3
\]

4. So we calculate \( A \):

\[
A = 2800 \left(1.014\right)^{3}
\]

5. Calculate \( (1.014)^{3} \):

\[
(1.014)^3 \approx 1.0425
\]

6. Now multiply by the principal:

\[
A \approx 2800 \times 1.0425 \approx 2920
\]

After rounding to two decimal places, we find that Harley will owe approximately \$2920 when he begins making payments.

So, the closest answer from the options provided is:

**D. \$2919.25**