To help pay for art school Keith borrowed money from an online lending company he took out a personal amortized loan for $50,000 at an interest rate of 5.7% with monthly payments for a term of 20 years for each part do not round any intermediate computations and round your final answers to the nearest cent if necessary refer to the list of financial formulas find Keith monthly payment
To find Keith's monthly payment, we can use the amortized loan formula for calculating the regular payment on a loan:
P = (r * PV) / (1 - (1 + r)^(-n))
Where:
P = monthly payment
r = monthly interest rate (annual interest rate divided by 12)
PV = present value of the loan (in this case, $50,000)
n = total number of payments (in this case, 20 years * 12 months per year)
First, let's calculate the monthly interest rate:
r = 5.7% / 100 / 12 = 0.00475
Then, calculate the total number of payments:
n = 20 years * 12 months per year = 240
Now, we can plug in the values into the formula:
P = (0.00475 * $50,000) / (1 - (1 + 0.00475)^(-240))
Calculating this using a calculator or spreadsheet, we find that Keith's monthly payment is approximately $361.63.
To find Keith's monthly payment, we can use the formula for calculating the monthly payment for an amortized loan. The formula is:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
where:
M = Monthly Payment
P = Principal Amount (loan amount)
r = Monthly Interest Rate
n = Number of Payments
Let's plug in the values for Keith's loan:
P = $50,000
r = 5.7% per year = 0.057 per month (convert to decimal)
n = 20 years * 12 months = 240 payments
Plugging in the values into the formula:
M = 50000 * (0.057 * (1 + 0.057)^240) / ((1 + 0.057)^240 - 1)
Now, let's calculate the monthly payment for Keith:
M ≈ $358.22
Therefore, Keith's monthly payment is approximately $358.22.