Multiple Choice
If Bruce waits for five years to begin paying back his loan, which time value of money concept is most relevant for calculating the present value of his future payments?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
If the interest rate on a fixed-payment loan increases while the monthly payment remains the same, what would be the impact on the number of months required to pay off the loan?
A
The number of months to pay off the loan would remain unchanged.
B
The loan would be paid off immediately.
C
The number of months to pay off the loan would increase.
D
The number of months to pay off the loan would decrease.
Verified step by step guidance1
Step 1: Understand the relationship between interest rates and loan payments. A fixed-payment loan means the monthly payment amount remains constant, regardless of changes in the interest rate.
Step 2: Recognize that an increase in the interest rate affects the portion of the monthly payment allocated to interest versus principal. Higher interest rates result in a larger portion of the payment going toward interest, leaving less to reduce the principal balance.
Step 3: Analyze the impact on the loan term. Since less of the monthly payment is applied to the principal, the principal balance decreases more slowly, requiring additional months to fully pay off the loan.
Step 4: Consider the mathematical formula for loan amortization. The formula for calculating the monthly payment includes the interest rate, loan amount, and loan term. If the interest rate increases while the payment remains fixed, the loan term must adjust to accommodate the slower reduction of the principal.
Step 5: Conclude that the number of months required to pay off the loan would increase due to the higher interest rate, as the fixed monthly payment is insufficient to maintain the original loan term.
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