The monthly payments for a $150,000 house with a 20% down payment and a 5.25% interest rate on a 15-year mortgage require the loan payment formula. An amortization schedule for six payments includes steps to calculate monthly interest, principal, and new balance.
To calculate the monthly payments on a mortgage, it is necessary to apply the formula for an amortizing loan:
M = P [ i(1+i)ⁿ ] / [ (1+i)ⁿ – 1 ]
Where:
M = monthly mortgage payment
P = the principle loan amount
i = monthly interest rate
n = number of months required to repay the loan
With a purchase price of $150,000 and a 20% down payment, we have:
- Down Payment = $150,000 * 20% = $30,000
- Loan Amount (P) = $150,000 - $30,000 = $120,000
- Annual Interest Rate = 5.25%
- Monthly Interest Rate (i) = 5.25% / 12 = 0.004375
- Loan Term = 15 years
- Number of Monthly Payments (n) = 15 * 12 = 180
Now we insert these numbers into the formula:
M = $120,000 [ 0.004375(1+0.004375)¹⁸⁰ ] / [ (1+0.004375)¹⁸⁰⁻¹ ]
After computing the above equation, we get the monthly mortgage payment M (exact computation required).
Creating an amortization schedule requires calculating the interest and principal portions of each payment for the first six months. These calculations are based on the remaining balance each month and the monthly interest rate:
- Calculate the interest for the current month by multiplying the current balance by the monthly interest rate.
- Subtract the interest from the total monthly payment to get the principal payment for that month.
- Subtract the principal payment from the remaining balance to get the new balance for the next month.
- Repeat steps 1 to 3 for each month.
Since the specific calculations for part b depend on having the exact monthly payment obtained from part a, those will have to be performed once the monthly payment value is precisely determined.