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
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 find the total amount of interest Keith will pay over the 20-year term, we can calculate the monthly payment and then subtract the principal amount borrowed.
Step 1: Convert the annual interest rate to a monthly interest rate.
Monthly interest rate = (Annual interest rate / 100) / 12 = (5.7 / 100) / 12 = 0.00475
Step 2: Calculate the number of monthly payments over the 20-year term.
Number of monthly payments = 20 years * 12 months/year = 240 months
Step 3: Calculate the monthly payment using the loan amount, monthly interest rate, and number of payments, using the amortization formula.
Monthly payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where P is the loan amount, r is the monthly interest rate, and n is the number of monthly payments.
P = $50,000
r = 0.00475
n = 240
Monthly payment = 50000 * (0.00475 * (1 + 0.00475)^240) / ((1 + 0.00475)^240 - 1)
≈ $341.87
Step 4: Calculate the total amount of interest paid over the 20-year term.
Total interest = (Monthly payment * Number of payments) - Principal amount borrowed
Total interest = (341.87 * 240) - 50000
Total interest ≈ $22,248.80
Therefore, Keith will pay approximately $22,248.80 in interest over the 20-year term.