Question

Sam is comparing the costs of two loans. The principal amount of each loan is $5,000. One is due in one year and the other is due in four years. Both have the same stated rate of annual interest. Which of the following is truea. the princpal paid for the one-year loan will be lower than the princpal paid for the four-year loanb. the princpal paid for the one-year loan will be higher than the princpal paid for the four-year loanc. the interest charges for the one-year loan will be higher than the interest charges for the four-year loand. the interest charges for the one-year loan will be lower than the interest charges for the four-year loane. the interest charges and princpal payments cannot be compared for the two loans

Answer 1

Answer:

b. the princpal paid for the one-year loan will be higher than the princpal paid for the four-year loan

d. the interest charges for the one-year loan will be lower than the interest charges for the four-year loan

Explanation:

Sam is comparing the costs of two loans.

The principal amount of each loan is $5,000.

One is due in one year and the other is due in four years.

Both have the same stated rate of annual interest.

Two of the following are true:

b. the principal paid for the one-year loan will be higher than the principal paid for the four-year loan.

Considering the time value of money, $5000 principal repayment in one year time discounted at 5% will be 5000/1.05^1 = $4,761 but if repaid in 4 years = 5000/ 1.05^4 = $4,113.5

d. the interest charges for the one-year loan will be lower than the interest charges for the four-year loan

5% on 5,000 for 1 year = $250 but if paid for 4 years will be 250 x 4 = $1000

Answer 2

Answer:

D) the interest charges for the one-year loan will be lower than the interest charges for the four-year loan

Explanation:

Even though the principal and the APR are the same for both loans, the duration of the loans change the total interest charged by the lender. The longer the repayment period, the most interests you are going to pay.

We can use a loan calculator to determine the total interest charged on both loans:

• loan 1, principal = $5,000, interest rate = 10%, n = 1 year ⇒ total interest charged = $274.95
• loan 2, principal = $5,000, interest rate = 10%, n = 4 years ⇒ total interest charged = $1,087.02

The monthly payment is lower for the second loan, but the total interest paid during the four years is much higher.