To help open up a wine bar Shen borrowed money from his credit union he took out a personal aortized loan for 43,000 at an interest rate of 6.55% with monthly payments for a term of 8 years for each part do not round any intermediate computations around your final answers to the nearest cent if she 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 Shen will pay, we first need to calculate the monthly payment for the loan.
The loan amount is $43,000.
The interest rate is 6.55% per year, or 0.0655 as a decimal.
The term of the loan is 8 years, or 8*12 = 96 months.
Let's use the formula to calculate the monthly payment for an amortized loan:
Monthly Payment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
P = Loan amount
r = Monthly interest rate
n = Number of payments
So, plugging in the values:
P = $43,000
r = 0.0655/12 (monthly interest rate)
n = 96
Monthly Payment = (43000 * (0.0655/12) * (1 + (0.0655/12))^96) / ((1 + (0.0655/12))^96 - 1)
Calculating the monthly payment using the equation mentioned above gives us approximately $601.32.
Now, let's calculate the total interest paid over the term of the loan:
Total Interest Paid = (Monthly Payment * Number of Payments) - Loan Amount
Total Interest Paid = ($601.32 * 96) - $43,000
Total Interest Paid ≈ $19,884.65 (rounded to the nearest cent)
Therefore, Shen will pay approximately $19,884.65 in interest over the term of the loan.
To find the total amount of interest Shen will pay on the loan, we need to calculate the total payment he will make over the 8-year term and subtract the borrowed amount.
Step 1: Convert the annual interest rate to a monthly rate.
Monthly interest rate = Annual interest rate / 12
Monthly interest rate = 6.55% / 12 = 0.00546
Step 2: Calculate the number of months in the loan term.
Loan term in months = 8 years * 12 months/year
Loan term in months = 96 months
Step 3: Calculate the monthly payment.
Monthly payment = Principal * Monthly interest rate / (1 - (1 + Monthly interest rate)^(-Loan term in months))
Monthly payment = 43,000 * 0.00546 / (1 - (1 + 0.00546)^(-96))
Monthly payment = 507.97
Step 4: Calculate the total payment over the loan term.
Total payment = Monthly payment * Loan term in months
Total payment = 507.97 * 96
Total payment = 48,764.32
Step 5: Calculate the total interest paid.
Total interest paid = Total payment - Principal
Total interest paid = 48,764.32 - 43,000
Total interest paid = 5,764.32
Therefore, Shen will pay a total of $5,764.32 in interest over the 8-year term.