Question

Mr. Peterson wrote a check of $7,820 to pay off a loan, which was given to him at a rate of 5% simple interest for 3 years. How much money did he borrow originally?

(a) $5,400
(b) $6,800
(c) $3,240
(d) $14,620

Answer 1

Mr. Peterson originally borrowed $6,800. This was determined by dividing the total amount paid ($7,820) by the sum of 1 plus the product of the interest rate (5%) and the time period (3 years), and then solving for the principal amount.

Step-by-step explanation:

To find out the original amount Mr. Peterson borrowed, we need to calculate the principal amount from the amount he paid off, which includes the original sum plus the simple interest. The formula for calculating simple interest is Interest = Principal × rate × time. Given that the interest rate is 5% (or 0.05 when expressed as a decimal) and the time is 3 years, we can rearrange the formula to solve for the principal: Principal = (Total payment)/(1 + (rate × time)).

Thus, we calculate the principal as follows:
Principal = $7,820 / (1 + (0.05 × 3))
Principal = $7,820 / (1 + 0.15)
Principal = $7,820 / 1.15
Principal = $6,800

Therefore, Mr. Peterson originally borrowed $6,800.