A man has a five-year old loan with which he purchased his house: his interest rate is 18% compunded monthly. Since he obtained this loan, interest rates have dropped and he can now get a loan for 13.2% compunded monthly. Because of this he is considering refinancing his home. The existing loan is a 15-year amortized loan for 6 million rupees and the new loan would be a 10-year loan for the current amount due on the old loan.
Find his monthly payment with the existing loan
Find the loan amount for the new loan
Find the monthly payment with his new loan
Find the total interest he will pay if he does not get a new loan
Find the total interest he will pay if he does get the new loan
To answer these questions, we need to use the formula for calculating monthly loan payments and the formula for calculating the future value of an annuity.
1. Monthly payment with the existing loan:
To calculate the monthly payment with the existing loan, we can use the formula for loan payments:
P = [(r * PV) / (1 - (1 + r)^(-n))]
Where:
P = Monthly payment
r = Monthly interest rate (annual interest rate / 12)
PV = Present value (loan amount)
n = Number of monthly payments (loan term in years * 12)
Given:
r = 18% compounded monthly = 18 / (12 * 100)
PV = 6 million rupees
n = 15 years * 12
Substituting the values into the formula, we get:
P = [(0.18/12) * 6,000,000] / (1 - (1 + (0.18/12))^(-15*12))
Calculate the value of P to find the monthly payment with the existing loan.
2. Loan amount for the new loan:
The loan amount for the new loan would be the current amount due on the old loan. Since the man is considering refinancing, the loan amount remains the same at 6 million rupees.
3. Monthly payment with the new loan:
To calculate the monthly payment with the new loan, we can use the same loan payment formula as in question 1, but with the new interest rate.
Given:
r = 13.2% compounded monthly = 13.2 / (12 * 100)
PV = 6 million rupees
n = 10 years * 12
Substitute the values into the formula to find the monthly payment with the new loan.
4. Total interest paid if he does not get a new loan:
To find the total interest paid if he does not get a new loan, we can use the formula for calculating the total interest paid on a loan:
Total Interest = (Monthly Payment * Number of Payments) - PV
Given:
Monthly Payment (from question 1)
Number of Payments = 15 years * 12
PV = 6 million rupees
Substitute the values into the formula to find the total interest paid if he does not get a new loan.
5. Total interest paid if he does get the new loan:
To find the total interest paid if he does get the new loan, we can use the same formula as in question 4, but with the new loan term (10 years * 12) and monthly payment (from question 3).
Substitute the values into the formula to find the total interest paid if he does get the new loan.
By following these steps and calculations, you will be able to find the answers to the given questions.