4. Vanna has just financed the purchase of a home for $200 000. She agreed to repay the loan by making equal monthly blended payments of $3000 each at 9%/a, compounded monthly.
Determine how much interest she will pay for her loan.
h. How much would Vanna have saved if she had obtained a loan at 7%/a, compounded monthly?
Can anyone give me the formulas please ? I can do the rest myself...
Certainly! In order to answer these questions, we can use the formula for calculating the monthly payment of a loan and the formula for calculating the total interest paid on a loan.
The formula for calculating the monthly payment of a loan is:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Principal amount (loan amount)
r = Monthly interest rate (annual interest rate divided by 12)
n = Total number of payments (number of years multiplied by 12)
The formula for calculating the total interest paid on a loan can be derived from the monthly payment formula. It is:
Total Interest = (M * n) - P
Now let's apply these formulas to solve the given questions.
1. Determine how much interest Vanna will pay for her loan.
Given:
Loan amount (P) = $200,000
Monthly payment (M) = $3,000
Annual interest rate (r) = 9%
Compounding frequency = monthly
Step 1: Convert the annual interest rate to the monthly interest rate.
r = 9% / 100 / 12 = 0.0075
Step 2: Calculate the total number of payments.
n = Total number of years * 12 = Unknown in this case
In order to find the total number of payments, we need to know the loan term (number of years).
Step 3: Calculate the monthly payment with the given information.
Using the formula for the monthly payment:
$3,000 = $200,000 * (0.0075 * (1 + 0.0075)^n) / ((1 + 0.0075)^n - 1)
Step 4: Calculate the total interest paid.
Total Interest = (Monthly payment * Total number of payments) - Principal amount
2. Determine how much Vanna would have saved if she had obtained a loan at 7%, compounded monthly.
Given:
Loan amount (P) = $200,000
Monthly payment (M) = $3,000
Annual interest rate (r) = 7%
Compounding frequency = monthly
Using the same steps as above, calculate the monthly payment and total interest paid using the formula.
Remember to substitute the new interest rate (7%) into the formula.
By comparing the total interest paid for the two cases, you can determine how much Vanna would have saved by obtaining a loan at 7% instead of 9%.
Please note that the total number of payments (n) is necessary to fully solve the questions. Once you know the term of the loan in years, multiply it by 12 to get the total number of payments.