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 if Keith pays the monthly payment each month for the full term find his total amount to repay the loan
To find Keith's total amount to repay the loan, we need to calculate the monthly payment and then multiply it by the number of months in 20 years.
First, let's calculate the monthly interest rate:
Monthly interest rate = Annual interest rate / 12
Monthly interest rate = 5.7% / 100 / 12 = 0.00475 (rounded to 5 decimal places)
Next, let's calculate the number of monthly payments:
Number of monthly payments = Number of years * 12
Number of monthly payments = 20 * 12 = 240
Now, let's calculate the monthly payment using the formula for the amortized loan:
Monthly payment = (loan amount * monthly interest rate) / (1 - (1 + monthly interest rate)^(-number of monthly payments))
Monthly payment = (50000 * 0.00475) / (1 - (1 + 0.00475)^(-240)) ≈ $361.80
Finally, let's calculate the total amount to repay the loan:
Total amount to repay = Monthly payment * Number of monthly payments
Total amount to repay = 361.80 * 240 ≈ $86,832
To calculate Keith's total amount to repay the loan, we need to consider the monthly payment amount and the term of the loan.
First, we need to calculate the monthly interest rate. The interest rate of 5.7% needs to be converted to a monthly rate. We divide it by 100 and then by 12 (number of months in a year).
Monthly interest rate = (5.7 / 100) / 12 = 0.00475
Next, we determine the total number of monthly payments. Since Keith has a loan term of 20 years, and there are 12 months in a year, the total number of payments is:
Total number of payments = 20 years * 12 months/year = 240 months
Now, we can calculate the monthly payment using the formula for an amortized loan:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Total number of payments))
Plugging in the values:
Monthly Payment = ($50,000 * 0.00475) / (1 - (1 + 0.00475)^(-240))
By solving this equation, we find that Keith's monthly payment is $329.80.
Finally, to calculate the total amount to repay the loan, we multiply the monthly payment by the total number of payments:
Total Amount to Repay = Monthly Payment * Total number of payments
Total Amount to Repay = $329.80 * 240 = $79,152
Therefore, Keith's total amount to repay the loan is $79,152.