To help open up a wine bar Shen borrowed money from his credit union he took out a personal amortized loan for 43,000 and interest rate of 6.55% with monthly payments for a term of eight 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 what is Shane's monthly payment
To calculate Shane's monthly payment for the personal amortized loan, we can use the formula for calculating the monthly payment of a loan with equal monthly installments.
Monthly Payment = P * (r * (1+r)^n) / ((1+r)^n - 1)
Where:
P = Principal amount of the loan
r = Monthly interest rate
n = Total number of payments
Given:
Principal amount (P) = $43,000
Interest rate (r) = 6.55% = 0.0655 (converted to decimal)
Number of payments (n) = 8 years * 12 months/year = 96 months
Substituting the values into the formula:
Monthly Payment = 43000 * (0.0655 * (1+0.0655)^96) / ((1+0.0655)^96 - 1)
Calculating this expression will give us Shane's monthly payment for the loan.
To calculate Shen's monthly payment for the personal amortized loan, we need to use the formula for the monthly payment on a loan:
PMT = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
PMT = Monthly payment
P = Loan amount (principal)
r = Monthly interest rate
n = Total number of payments
Let's plug in the values given:
P = $43,000
r = 6.55% per year = 6.55 / 100 / 12 = 0.00545833 per month (monthly interest rate)
n = 8 years * 12 months = 96 months
PMT = (43,000 * 0.00545833 * (1 + 0.00545833)^96) / ((1 + 0.00545833)^96 - 1)
Now, let's calculate it step-by-step:
Step 1: Calculate (1 + r)^n
(1 + 0.00545833)^96 = 1.71061828
Step 2: Calculate (1 + r)^n - 1
(1.71061828 - 1) = 0.71061828
Step 3: Calculate (43,000 * 0.00545833 * (1.71061828)) / 0.71061828
= $1061.76259961
Round the final answer to the nearest cent:
Shen's monthly payment for the personal amortized loan is approximately $1061.76.