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 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 and then multiply it by the number of months in the term.
First, we convert the annual interest rate to a monthly rate. The monthly interest rate is 5.7% / 12 months = 0.475%.
Next, we calculate the number of months in the term. 20 years * 12 months/year = 240 months.
To calculate the monthly payment using the loan amortization formula, we can use the following formula:
Monthly Payment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
where:
P = loan amount = $50,000
r = monthly interest rate = 0.475%
n = number of months = 240
Plugging in the values, we get:
Monthly Payment = (50000 * 0.00475 * (1 + 0.00475)^240) / ((1 + 0.00475)^240 - 1)
Using a financial calculator or spreadsheet, the monthly payment is approximately $326.72.
To find the total amount of interest paid, we multiply the monthly payment by the number of months:
Total Interest = Monthly Payment * Number of Months
Total Interest = $326.72 * 240
Total Interest = $78,412.80
Therefore, Keith will pay a total of $78,412.80 in interest over the term of the loan.
To find the total amount of interest Keith will pay, we need to use the formula for calculating the total interest on an amortized loan:
Total Interest = (Monthly Payment * Number of Payments) - Loan Amount
1. Calculate the number of payments:
Number of Payments = Number of Years * Number of Months per Year
Number of Payments = 20 * 12
Number of Payments = 240
2. Calculate the monthly interest rate:
Monthly Interest Rate = Annual Interest Rate / Number of Months per Year
Monthly Interest Rate = 5.7% / 12
Monthly Interest Rate = 0.057 / 12
Monthly Interest Rate = 0.00475
3. Calculate the monthly payment using the formula for an amortized loan:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments))
Monthly Payment = ($50,000 * 0.00475) / (1 - (1 + 0.00475)^(-240))
Monthly Payment = $296.38 (rounded to the nearest cent)
4. Calculate the total interest paid:
Total Interest = (Monthly Payment * Number of Payments) - Loan Amount
Total Interest = ($296.38 * 240) - $50,000
Total Interest = $71,121.20 - $50,000
Total Interest = $21,121.20
Therefore, Keith will pay a total of $21,121.20 in interest over the life of the loan.