Suppose you borrow $359,000 for a home loan.The interest rate is 9% per annum nominal, and the loan is for 25 years.If you make monthly repayments, how much is each repayment?Round your final answer to 2 decimal places. E.g. if the final answer is $12345.8342, please type 12345.83 in the answer box (do not type the dollar sign).
Question
Suppose you borrow 12345.8342, please type 12345.83 in the answer box (do not type the dollar sign).
Solution
To solve this problem, we need to use the formula for the monthly payment on a loan, which is P = [r*PV] / [1 - (1 + r)^-n], where:
- P is the monthly payment.
- r is the monthly interest rate (annual interest rate divided by 12).
- PV is the present value, or principal amount of the loan.
- n is the total number of payments (or months).
Here are the steps to solve the problem:
- Convert the annual interest rate to a monthly rate: 9% per annum is 0.09/12 = 0.0075 per month.
- Identify the principal amount of the loan: PV = $359,000.
- Identify the total number of payments: 25 years is 25*12 = 300 months.
- Plug these values into the formula to calculate the monthly payment: P = [0.0075*2,914.70.
So, each monthly repayment is approximately $2,914.70.
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