To calculate Carissa's monthly payment, we can use the formula for a loan payment:
PMT = P(r(1+r)^n) / ((1+r)^n - 1)
Where:
PMT = monthly payment
P = loan amount ($25,000)
r = monthly interest rate (5.4% / 12 = 0.0045)
n = total number of payments (10 years * 12 months = 120 payments)
PMT = $25000(0.0045(1+0.0045)^120) / ((1+0.0045)^120 - 1)
PMT = $25000(0.0045(1.0045)^120) / ((1.0045)^120 - 1)
PMT = $25000(0.0045(2.51264)) / (2.51264 - 1)
PMT = $25000(0.011306) / 1.51264
PMT = $282.66
Therefore, Carissa's monthly payment will be $282.66.
Now, let's fill in the amortization table for the first two months of the loan.
Payment Number | Interest | Principal | Balance
1 | | | $25,000
2 | | | $23,787.34
To fill in the table, we need to calculate the interest and principal portions of each payment.
For the first payment:
Interest = Balance * Monthly interest rate = $25,000 * 0.0045 = $112.50
Principal = Monthly payment - Interest = $282.66 - $112.50 = $170.16
New Balance = Old balance - Principal = $25,000 - $170.16 = $23,829.84
For the second payment:
Interest = Balance * Monthly interest rate = $23,829.84 * 0.0045 = $107.24
Principal = Monthly payment - Interest = $282.66 - $107.24 = $175.42
New Balance = Old balance - Principal = $23,829.84 - $175.42 = $23,654.42
By continuing this calculation for each payment, you can complete the amortization table for the entire loan term.
Carissa graduates from college with a loan of $25,000, which she will repay with equal monthly payments over the next 10 years. The interest rate is 5.4%.
How much is Carissa's monthly payment? Round your answer to the nearest cent.
Fill in the amortization table below for the first two months of the loan. Round entries to the nearest cent.
payment number, interest, principal, balance ($25000)
1
2
1 answer
1 answer