Your yearly loan repayments on a $250,000 loan over ten years are $34,776.17. If the interest rate is 6.5% p.a., what is the amount of principal repaid in the first year?

Question

Your yearly loan repayments on a $250,000 loan over ten years are $34,776.17.   If the interest rate is 6.5% p.a., what is the amount of principal repaid in the first year?

BlackTom AI · Accepted Answer

We are given a loan of $250,000 over ten years with yearly repayments of $34,776.17 and an annual interest rate of 6.5%. The task is to find the amount of principal repaid in the first year.

Option 1: $16,250.00
This value matches the annual interest portion only. The interest for the first year is 6.5% of 250,000, which equals 0.065 × 250,000 = 16,250. Since a loan payment consists of both interest and principal, this option would represent the interest component, not the principal repayment. Therefore this option is incorrect as the principal repaid is larger than the interest portion.

Option 2: $215,223.83
This number is far larger than the total annual payment and cannot be the principal repaid in the first year. The principal repaid in any year cannot exceed the total annual payment, and certainly cannot exceed the loan balance. Hence this option is incorrect due to being implausibly high relative to the payment amount.

Option 3: $18,526.17
This amount is obtained by subtracting the interest portion from the total payment. First compute the interest for the year: 6.5% of 250,000 = 16,250. Then principal repaid = total payment − interest = 34,776.17 − 16,250 = 18,526.17. This aligns with the definition of loan amortization where each payment covers interest plus some principal. Therefore this option is correct as it represents the principal component of the first-year payment.

Option 4: $231,473.83
This value is much larger than the annual payment and would imply a principal reduction far beyond the payment amount, which is impossible in a single year. It contradicts the basic premise that the yearly payment covers both interest and some principal. Thus this option is incorrect.

In summary, the correct interpretation is that the first-year principal repaid is the total payment minus the interest for that year, i.e., 34,776.17 − 16,250 = 18,526.17, which corresponds to Option 3.

Your yearly loan repayments on a $250,000 loan over ten years are $34,776.17. If the interest rate is 6.5% p.a., what is the amount of principal repaid in the first year? 单项选择题

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