Questions: Cost of Borrowing and Interest Mechanics

Question 1

Two car loans each cover $25,000 at the same annual interest rate. Loan A runs 3 years; Loan B runs 6 years and has a lower monthly payment. How do their total costs compare?

• A. They cost the same — identical rate means identical total interest
• B. Loan A costs more — higher monthly payments mean overpaying relative to the loan's value
• C. Loan B costs more — a longer term means more months of interest accruing on the outstanding balance
• D. It depends entirely on lender fees, not on the term or payment size

Answer: (C)

Longer terms produce lower monthly payments but higher total interest. Interest accrues on the outstanding balance for more periods; even at the same rate, more time means more total interest paid. Loan B's lower payment is not savings — it is a repackaging of the debt that transfers more money to the lender overall. The monthly payment is the least useful number for comparing true borrowing cost.

Question 2

Lender A offers a 5.8% rate with $5,000 in closing costs; Lender B offers 6.0% with no fees. The borrower plans to keep the loan for 30 years on a $300,000 mortgage. Which loan costs less overall?

• A. Lender B — zero closing costs mean a lower total outlay from day one
• B. Lender A — the lower rate compounds over 30 years, saving far more than the $5,000 fee gap
• C. They are equivalent — APR accounts for both rate and fees and would be identical
• D. Cannot be determined without knowing the exact amortization schedule

Answer: (B)

On a $300,000 loan, a 0.2% rate difference over 30 years saves roughly $12,000–$15,000 in total interest — far exceeding the $5,000 closing-cost difference. APR is the right comparison tool: it folds fees into an annualized rate, making this tradeoff explicit. A lower APR wins over a long holding period. The error in option A is anchoring on upfront cost rather than total cost.

Question 3

In the early years of an amortizing mortgage, most of each monthly payment reduces the principal balance.

• T. True
• F. False

Answer: False

Amortization works in reverse: early payments are mostly interest. Because the outstanding balance is at its maximum in the early years, the interest charge is highest. A typical 30-year mortgage might allocate 75–80% of the first payment to interest and only 20–25% to principal. The proportion gradually shifts over the loan's life — late payments are mostly principal. This is why you can pay for a decade and still owe nearly the original balance.

Question 4

Comparing loans by total interest paid (principal excluded) gives a more accurate picture of borrowing cost than comparing monthly payments alone.

• T. True
• F. False

Answer: True

Monthly payment hides term length — a lower payment often signals a longer loan with more total interest. Total interest paid is a far better proxy for true cost. The most accurate metric is APR, which also captures fees. Lenders are well aware that consumers anchor on monthly payment, which is precisely why they market loans using payment size rather than total cost.

Question 5

Why does a one-percentage-point difference in mortgage interest rate produce a much larger difference in total cost over 30 years than most borrowers expect?

Model answer: Because compound interest accrues on the full outstanding balance month after month for 30 years (360 payments). A 1% annual difference means about 0.083% more per month applied to a balance starting at hundreds of thousands of dollars. Each month's extra interest charge also means slightly less principal is paid down, keeping the balance higher for longer, generating even more interest. These small monthly differences accumulate into tens of thousands of dollars over the full term.

This is the compounding effect in reverse — working against the borrower. Intuition underestimates it because each individual month's difference is small, but the multiplication over 360 periods on a large balance is substantial. The $300k at 5% vs. 6% example ($279k vs. $347k in total interest) illustrates a $68,000 gap from a single percentage point.