To find the total amount that Keith needs to repay the loan, we first need to calculate his monthly payment.
We can use the formula for calculating the monthly payment on an amortized loan:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = monthly payment
P = principal loan amount
r = monthly interest rate (annual interest rate divided by 12)
n = total number of monthly payments
Let's calculate the monthly payment:
P = $50,000
r = 5.7% / 100 / 12 = 0.00475
n = 20 * 12 = 240
M = 50,000 * (0.00475 * (1 + 0.00475)^240) / ((1 + 0.00475)^240 - 1)
M ≈ $366.92
Keith's monthly payment is approximately $366.92.
Now, let's calculate the total amount to repay the loan:
Total amount = monthly payment * total number of monthly payments
Total amount = $366.92 * 240
Total amount ≈ $88,061.83
Therefore, Keith will need to repay a total of approximately $88,061.83.
To help pay for art school Keith borrowed money from an online lending company he took out a personal and 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 Keith pays the monthly payment each month for the full term find his total amount to repay the loan
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