Let's Practice
You have done some research on different auto loans with different interest rates, so now it is time to calculate simple interest on your own. Recall that the formula for simple interest is:
\( I = Prt \)
To determine the total amount of money to be paid back at the end of a loan you would use the following formula:
\( A = P(1 + rt) \)
For each of the practice questions below, determine the interest and/or the total amount. Remember that the interest rate percentage must be converted to a decimal (by dividing it by 100) and the time must be in years (by dividing months by 12). When ready, click each answer button to reveal the solution.
Let's look back at Ida. She can get a $20,000 loan for a car, to be paid off in two years, with an interest rate of 4%. If this interest is calculated using the simple interest formula, how much interest will Ida end up paying at the end of the two-year loan term?
Here, \( P = 20000,\ r = 0.04 \) (must change percent to a decimal), and \( t = 2 \). Now, substitute into the formula to solve:
\( I = 20000 \cdot 0.04 \cdot 2 = 1600. \)
This means, at the end of two years, Ida will have to pay $1,600 in interest.
Lance just agreed to a $10,000 loan for repairs on his house. The simple interest rate is 7% and the loan is to be paid back over an 18-month period. What is the total amount that Lance must pay on this loan?
Here, \( P = 10000,\ r = 0.07 \), and \( t = 1.5 \).
Convert the months to years by dividing the number of months by 12.
\( \mathrm{ 1.5\ years = \frac{18\ months}{12\ months} } \)
Now, substitute into the formula to solve:
\( A = \$ 10000(1 + \left( 0.07 \cdot 1.5 \right)) = \$ 11,050 \)
So, the total amount Lance must pay on an 18-month, $10,000 loan with a 7% simple interest rate, is $11,050.
Julian is excited because he has just finished paying back a $32,875 loan he had taken out.
If the total amount that Julian paid back was $39,980, what was the total simple interest on the loan?
Now, suppose the loan term was for 3 years. What was the interest rate on the loan? Round your answer to the nearest tenth percent.
The simple interest will be the total amount minus the principal:
\( \$ 39980 - \$ 32875 = \$ 7105. \)
The total simple interest on Julian's loan was $7,105.
Now, to find the interest rate on this loan if the term is three years, substitute the values into the simple interest formula and solve for \( r \), the interest rate:
\( P = 32875,\ t = 3 \), and \( I = 7105 \):
\( 7105 = 32875 \cdot r \cdot 3 \)
\( 7105 = 98625 \cdot r \)
\( 0.072 \approx r \)
So, the interest rate on this loan was 0.072, or 7.2%.
You researched two auto loans to get your first car. You can borrow $15,000 with simple interest. The loan details are:
| Loan 1 | Loan 2 | |
|---|---|---|
| rate | 6% | 4.5% |
| time | 3 years | 5 years |
Which loan, 1 or 2, will end up costing you less in interest?
First, calculate the simple interest for Loan 1:
\( P = 15000,\ r = 0.06 \), and \( t = 3 \).
Now, substitute into the formula to solve:
\( I = 15000 \cdot 0.06 \cdot 3 = 2,700 \)
So, if you choose Loan 1, you will end up paying $2,700 in interest.
Next, calculate the simple interest for Loan 2:
\( P = 15000,\ r = 0.045 \), and \( t = 5 \).
Now, substitute into the formula to solve:
\( I = 15000 \cdot 0.045 \cdot 5 = 3,375 \)
So, if you choose Loan 2, you will end up paying $3,375 in interest.
Since 2,700 < 3,375, you will pay less interest with Loan 1 than with Loan 2.
Question
When taking out a loan that uses simple interest, is it better to go for a longer loan term or a shorter loan term?
A shorter loan term means you will pay less in interest.
