This morning,you borrowed $150,000 to buy a house.The mortgage rate is 7.35 percent.The loan is to be repaid in equal monthly payments over 20 years.The first payment is due one month from today.How much of the second payment applies to the principal balance? (Assume that each month is equal to 1/12 of a year.)

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To find how much of the second payment applies to the principal balance, we first need to calculate the monthly payment amount using the loan amount, interest rate, and loan term. The formula for the monthly payment (M) on a fixed-rate mortgage is:$$M = P \frac{r(1+r)^n}{(1+r)^n - 1}$$where:- $P$ is the loan amount ($150,000),- $r$ is the monthly interest rate (annual rate divided by 12, so 7.35% / 12 = 0.06125 or 0.006125 as a decimal),- $n$ is the total number of payments (20 years * 12 months = 240).Plugging in the numbers:$$M = 150,000 \frac{0.006125(1+0.006125)^{240}}{(1+0.006125)^{240} - 1}$$$$M \approx 1,194.67$$This is the total monthly payment. To find out how much of the second payment applies to the principal, we need to calculate the interest portion of the first payment and subtract it from the total monthly payment to see how much of the first payment goes towards the principal. Then, we calculate the interest for the second month based on the reduced principal and subtract this new interest from the total monthly payment to find the principal portion of the second payment.Interest for the first month:$$Interest = Principal \times monthly\ rate = 150,000 \times 0.006125 = 917.50$$Principal portion of the first payment:$$Principal\ portion = Total\ monthly\ payment - Interest = 1,194.67 - 917.50 = 277.17$$After the first payment, the new principal balance is:$$New\ principal = Original\ principal - Principal\ portion\ of\ first\ payment = 150,000 - 277.17 = 149,722.83$$Interest for the second month:$$Interest = New\ principal \times monthly\ rate = 149,722.83 \times 0.006125 \approx 916.83$$Principal portion of the second payment:$$Principal\ portion = Total\ monthly\ payment - Interest = 1,194.67 - 916.83 \approx 277.84$$The closest answer to this calculation is $277.61, which is option B. The slight discrepancy in the final cent value is due to rounding during the calculation process.

This Morning,you Borrowed $150,000 to Buy a House