To help open up a wine bar Shane borrowed money from his credit union he took out a personal amortized 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 and round your final answers to the nearest cent what is shins monthly payment

Question

To help open up a wine bar Shane borrowed money from his credit union he took out a personal amortized 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 and round your final answers to the nearest cent what is shins monthly payment

Answer 1

To calculate Shane's monthly payment for his personal amortized loan, we can use the formula for loan amortization:

PMT = (P * r * (1 + r)^n) / ((1 + r)^n - 1)

Where:
PMT = monthly payment
P = principal amount borrowed ($43,000)
r = monthly interest rate (6.55% / 100 / 12)
n = total number of payments (8 years * 12 months/year)

First, let's calculate the monthly interest rate:
r = 6.55% / 100 / 12 = 0.005458333

Next, calculate the total number of payments:
n = 8 years * 12 months/year = 96

Now, let's substitute these values into the formula:

PMT = (43,000 * 0.005458333 * (1 + 0.005458333)^96) / ((1 + 0.005458333)^96 - 1)

Using a calculator, the monthly payment (rounded to the nearest cent) is approximately $577.84. Therefore, Shane's monthly payment for the loan is $577.84.

Answer 2

To calculate Shane's monthly payment, we can use the loan amortization formula:

Monthly Payment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)

Where:
P = Principal amount (loan amount) = $43,000
r = Monthly interest rate = Annual interest rate / 12 = 6.55% / 100 / 12
n = Total number of payments = 8 years * 12 months/year

Let's calculate the monthly payment step by step:

1. Calculate the monthly interest rate (r):
r = 6.55% / 100 / 12 = 0.00545833

2. Calculate the total number of payments (n):
n = 8 years * 12 months/year = 96

3. Calculate the numerator of the monthly payment formula:
Numerator = P * r * (1 + r)^n
= $43,000 * 0.00545833 * (1 + 0.00545833)^96

4. Calculate the denominator of the monthly payment formula:
Denominator = (1 + r)^n - 1
= (1 + 0.00545833)^96 - 1

5. Calculate the monthly payment:
Monthly Payment = Numerator / Denominator

Now let's calculate the monthly payment:

Numerator = $43,000 * 0.00545833 * (1 + 0.00545833)^96
Denominator = (1 + 0.00545833)^96 - 1
Monthly Payment = Numerator / Denominator

Monthly Payment ≈ $581.30

Therefore, Shane's monthly payment is approximately $581.30.