Question

Gideon took out an R150 000 loan this morning, to buy a house. The interest rate on a mortgage is 7,35%. 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.)

Answer 1

Explanation:

To solve this problem, we can use the formula for calculating the fixed monthly payment on a mortgage:

P = (r * PV) / (1 - (1 + r)^(-n))

where:

P = fixed monthly payment

r = monthly interest rate (annual interest rate divided by 12)

PV = present value of the loan (loan amount)

n = total number of payments (number of years multiplied by 12)

Using the given values:

r = 0.0735 / 12 = 0.006125

PV = R150,000

n = 20 x 12 = 240

Then we can calculate the monthly payment:

P = (0.006125 * 150000) / (1 - (1 + 0.006125)^(-240)) = R1,181.91

This means that Gideon will have to pay R1,181.91 every month for 20 years to repay his loan.

To determine how much of the second payment applies to the principal balance, we need to calculate the interest and principal amounts of the first payment.

For the first payment, the interest can be calculated as:

interest1 = r * PV = 0.006125 * 150000 = R918.75

This means that the first payment consists of R918.75 in interest and the rest, R1,181.91 - R918.75 = R263.16 is principal.

To find out how much of the second payment applies to the principal balance, we need to subtract the interest and add the calculated principal amount from the first payment to the amount of the second payment:

principal2 = (P - interest1) + principal1 = (1181.91 - 918.75) + 263.16 = R525.32

Therefore, R525.32 of the second payment applies to the principal balance.