Louise Grantham is buying a home for $198,500 with a 20% down payment. She has a 5.75% loan for 25 years. Create amortization schedule for the first two months of her loan.
P = (Po*r*t)/(1-(1+r)^-t).
100% 20% = 80% = 0.8
Po = 0.8 * 198,500 = $158,800
r = (5.75%/12)/100% = 0.00479 Monthly %
rate.
t = 25yrs. * 12mo/yr. = 300 Months.
Plug the given values into the Eq and
get: P = $299,706.29
I=P-Po=299,706.29 - 158,800=$140,906.29,
Total.
Monthly Payments = P/t = 299,706.29/300=
$999.02
Amortization Table:
Payment---Int.---Prin.---Bal.
00.00-----0.00---0.00----$158,800.00
999.02----760.92-238.10--$158,561.90
999.02----759.78-239.24--$158,322.66
Amortization Calculations: t = 1 Month.
1. I = Po*r*t = 158,800*(0.0575/12)*1 =
760.92
Prin. = 999.02-760.92 = 238.10
Bal. = 158,800-238.10 = $158,651.90
2. I = Po2*r*t=158,561.90*(0.0575/12)*1=
$759.78
Prin. = 999.02-759.78 = $239.24
Bal. = 158,561.90-239.24 = $158,322.66
To create an amortization schedule, we need to calculate the monthly mortgage payment and then break down the payment into principal and interest amounts for each month. Here's how you can do it step by step:
1. Calculate the loan amount:
The down payment is 20%, so the loan amount is 80% of $198,500.
Loan amount = 80% of $198,500 = $158,800.
2. Calculate the monthly interest rate:
The annual interest rate is 5.75%, so the monthly interest rate is 5.75% divided by 12.
Monthly interest rate = 5.75% / 12 = 0.00479.
3. Calculate the number of payments:
The loan term is 25 years, so the total number of payments is 25 years multiplied by 12 months.
Number of payments = 25 * 12 = 300.
4. Calculate the monthly mortgage payment using the loan amount, monthly interest rate, and number of payments:
Monthly mortgage payment formula:
M = P * r * (1 + r)^n / ((1 + r)^n - 1)
where M is the monthly mortgage payment
P is the loan amount
r is the monthly interest rate
n is the number of payments
Monthly mortgage payment = $158,800 * 0.00479 * (1 + 0.00479)^300 / ((1 + 0.00479)^300 - 1)
Monthly mortgage payment ≈ $967.79
5. Create the amortization schedule:
Now we can start creating the amortization schedule for the first two months.
Month 1:
Starting Balance = Loan amount ($158,800)
Monthly Interest = Starting Balance * Monthly Interest Rate
Principal Payment = Monthly Mortgage Payment - Monthly Interest
Ending Balance = Starting Balance - Principal Payment
Month 2:
Starting Balance = Ending Balance from previous month
Repeat the calculations for Monthly Interest, Principal Payment, and Ending Balance.
Here's the amortization schedule for the first two months of Louise Grantham's loan:
Month | Starting Balance | Monthly Interest | Principal Payment | Ending Balance
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1 | $158,800 | $636.97 | $330.82 | $158,469.18
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2 | $158,469.18 | $635.73 | $332.06 | $158,137.12
Note: The values in the amortization table have been rounded for simplicity.