Question

Stacey wants to secure a loan of $150,000 to purchase a house. Her bank is offering her an interest rate of 5.25%. Given that she can afford monthly payments of $1,000, what should be the duration of her loan in years, rounded to the nearest tenth?

Answer 1

To find the duration of Stacey's loan, the loan amortization formula is used, accounting for the loan amount, the monthly payment, and the annual interest rate. The total number of monthly payments is calculated and then converted into years, rounding to the nearest tenth.

Step-by-step explanation:

To determine the duration of Stacey's loan in years, we need to use the loan amortization formula. This formula factors in the loan amount, the monthly payment, and the annual interest rate to calculate the amount of time needed to pay off the loan.

The monthly interest rate is 5.25% divided by 12, which equals to approximately 0.4375% per month. We can use the following amortization formula:

number of payments = (-ln(1 - (loan amount * monthly interest rate) / monthly payment)) / ln(1 + monthly interest rate)

Plugging the values into the formula gives us:

number of payments = (-ln(1 - (150,000 * 0.004375) / 1,000)) / ln(1 + 0.004375)

After calculating, we can determine the total number of months, and then divide by 12 to find the duration in years. We would round the figure to the nearest tenth to provide Stacey with her answer.