To find the total amount of interest Keith will pay, we need to calculate the monthly payment amount first.
First, we convert the interest rate from an annual rate to a monthly rate by dividing it by 12 months:
5.7% / 12 = 0.475% (monthly interest rate)
Next, we calculate the monthly payment using 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 = Loan amount
r = Monthly interest rate (in decimal form)
n = Number of payments
Plugging in the given values:
P = $50,000
r = 0.475% = 0.00475
n = 20 years * 12 months/year = 240 months
M = $50,000 * (0.00475 * (1+0.00475)^240) / ((1+0.00475)^240 - 1)
Calculating this expression, we find that the monthly payment amount is approximately $331.03.
To find the total amount of interest paid, we need to calculate the total amount paid over 20 years and subtract the original loan amount.
Total amount paid = Monthly payment * Number of payments
Total amount paid = $331.03 * 240 months
Total amount paid = $79,447.20
Total interest paid = Total amount paid - Loan amount
Total interest paid = $79,447.20 - $50,000
Total interest paid = $29,447.20
Therefore, Keith will pay a total of approximately $29,447.20 in interest over the 20-year term.
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 Keith pays the monthly payment each month for the full term find the total amount of interest he will pay
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