If the loan payments and interest rate remain unchanged, will it take longer to reduce the balance from $20,000 to $10,000 than to reduce the balance from $10,000 to $0? Explain briefly.

Question

Quizplus · Accepted Answer

With each successive payment, the interest component becomes smaller and the principal component becomes larger. Therefore, the total principal repaid in the first half of the amortization period will be less than the total principal repaid in the second half of the amortization period. It follows that: 
(1) less than half of the original principal will be repaid in the first half of the amortization period; and 
(2) it will take more than half of the amortization period to reduce the balance to half the original principal.

If the Loan Payments and Interest Rate Remain Unchanged, Will