Sarah is planning to purchase a new house. To purchase the house, she will need to borrow $550,000 from the bank. The loan term is 30 years and the terms of the contract require monthly end of period payments (including interest and principle). The current interest rate offered by her bank is 3.5% per annum for a variable rate mortgage loan. If Sarah borrows the money from her bank and the interest rate decreases by 0.5% three years after the mortgage started, what would the new monthly repayment be?Question 1Select one:a.$1,375.00b.$2,469.75c.$2,500.00d.$2,331.00
Question
Sarah is planning to purchase a new house. To purchase the house, she will need to borrow 1,375.00b.2,500.00d.$2,331.00
Solution
To answer this question, we first need to calculate the initial monthly payment using the original interest rate, then adjust it for the new interest rate after 3 years.
Step 1: Calculate the initial monthly payment The formula for calculating the monthly payment on a loan is:
P = [r*PV] / [1 - (1 + r)^-n]
where: P = monthly payment r = monthly interest rate (annual rate / 12) PV = present value, i.e., the loan amount n = total number of payments, or loan term in months
Using the given values: r = 3.5% / 12 / 100 = 0.002917 PV = $550,000 n = 30 years * 12 months/year = 360 months
P = [0.002917 * 550,000] / [1 - (1 + 0.002917)^-360] = $2,469.70
Step 2: Calculate the new monthly payment after the interest rate decrease Three years after the mortgage started, the interest rate decreases by 0.5%. So, the new monthly interest rate is:
r = (3.5% - 0.5%) / 12 / 100 = 0.0025
Also, the remaining loan term at this point is:
n = (30 years - 3 years) * 12 months/year = 324 months
Substitute the new values of r and n into the formula:
P = [0.0025 * 550,000] / [1 - (1 + 0.0025)^-324] = $2,158.96
So, the new monthly repayment would be approximately $2,158.96. This option is not listed in the given choices, so there might be a mistake in the question or the provided options.
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