Richard borrowed 180000 dollars from his bank to help finance the purchase of a house. The bank charges interest a rate of 5.9 percent per year compounded monthly. Richard has agreed to repay the loan in equal monthly installments over 25 years.
How much should each payment be if the loan is to be amortized at the end of the term?
To find the amount of each monthly payment, we can use the amortization formula:
P = (r * PV) / (1 - (1 + r) ^ -n),
where:
P = monthly payment,
r = monthly interest rate,
PV = present value of the loan,
n = total number of payments.
First, we need to convert the annual interest rate to a monthly interest rate. Since the compounding is monthly, the monthly interest rate is 5.9% divided by 12, which is 0.059 / 12 = 0.004917.
Second, we calculate the total number of payments. Since Richard has agreed to repay the loan over 25 years, the total number of payments is 25 years multiplied by 12 months, which is 25 * 12 = 300.
Next, we substitute the values into the formula:
P = (0.004917 * 180000) / (1 - (1 + 0.004917) ^ -300).
Calculating this expression will give us the value of P, which represents the monthly payment.