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
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 find the total amount Keith will repay on the loan, we need to calculate the monthly payment and then multiply it by the number of months in the term.
Step 1: Calculate the monthly interest rate.
The annual interest rate is 5.7%. To get the monthly interest rate, divide it by 12 (number of months in a year).
Monthly interest rate = 5.7% / 12 = 0.057 / 12 = 0.00475
Step 2: Calculate the number of months in the term.
The loan term is 20 years. To get the number of months, multiply it by 12.
Number of months = 20 years * 12 months/year = 240 months
Step 3: Calculate the monthly payment using the loan amount, interest rate, and number of months.
We can use the loan amortization formula to calculate the monthly payment. The formula is:
Monthly payment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
P = Loan amount = $50,000
r = Monthly interest rate = 0.00475
n = Number of months = 240
Monthly payment = (50000 * 0.00475 * (1 + 0.00475)^240) / ((1 + 0.00475)^240 - 1)
Using a calculator or spreadsheet, the monthly payment comes out to be approximately $338.99
Step 4: Calculate the total amount repaid.
Total amount repaid = Monthly payment * Number of months
Total amount repaid = $338.99 * 240 = $81,357.60
Therefore, Keith will repay a total of approximately $81,357.60 over the 20-year term.