To repay the loan over two years, there will be a total of 24 monthly payments (12 payments per year * 2 years).
The interest is compounded semi-annually, so the interest rate for each period will be 7%/2 = <<7/2=3.5>>3.5%.
To calculate the size of each monthly payment, we can use the monthly payment formula for a loan:
M = P * (r(1+r)^n) / ((1+r)^n - 1)
Where:
M = Monthly payment
P = Principal loan amount
r = Monthly interest rate
n = Number of payments
Substituting the given values into the formula, we get:
M = $20,000 * (0.035(1+0.035)^24) / ((1+0.035)^24 - 1)
M = $20,000 * 0.035 * 1.419826 / (1.419826 - 1)
M = $20,000 * 0.0496672291 / 0.419826
M = $2,668.67
Therefore, the size of each monthly payment is $2,668.67.
Ralph's Machine Shop purchased a computer to use in tuning engines. To finance the purchase, the company borrowed $20,000 at 7% compounded semi-annually. To repay the loan, equal monthly payments are made over two years, with the first payment due one year after the date of the loan. What is the size of each monthly payment?
3 answers
Ralph's Machine Shop purchased a computer to use in tuning engines. To finance the purchase, the company borrowed $20,000 at 7% compounded semi-annually. To repay the loan, equal monthly payments are made over two years, with the first payment due one year after the date of the loan. What is the size of each monthly payment?
To find the size of each monthly payment, we need to calculate the loan repayment amount.
The loan is for $20,000 at an annual interest rate of 7% compounded semi-annually. This means that after one year, the loan will accrue interest and the principal will grow.
First, let's calculate the interest earned on the loan after one year:
Annual interest rate = 7%
Semi-annual interest rate = 7% / 2 = 3.5%
Interest earned after one year = $20,000 * 3.5% = $20,000 * 0.035 = $700
Now, let's calculate the remaining loan balance after one year:
Principal loan amount = $20,000
Remaining balance after one year = Principal loan amount + Interest earned after one year
Remaining balance after one year = $20,000 + $700 = $20,700
The loan needs to be repaid over 2 years, which is equivalent to 24 months.
To calculate the size of each monthly payment, we divide the remaining balance by the number of months:
Monthly payment = Remaining balance / Number of months
Monthly payment = $20,700 / 24
Monthly payment ≈ $862.50
Therefore, the size of each monthly payment is approximately $862.50.
The loan is for $20,000 at an annual interest rate of 7% compounded semi-annually. This means that after one year, the loan will accrue interest and the principal will grow.
First, let's calculate the interest earned on the loan after one year:
Annual interest rate = 7%
Semi-annual interest rate = 7% / 2 = 3.5%
Interest earned after one year = $20,000 * 3.5% = $20,000 * 0.035 = $700
Now, let's calculate the remaining loan balance after one year:
Principal loan amount = $20,000
Remaining balance after one year = Principal loan amount + Interest earned after one year
Remaining balance after one year = $20,000 + $700 = $20,700
The loan needs to be repaid over 2 years, which is equivalent to 24 months.
To calculate the size of each monthly payment, we divide the remaining balance by the number of months:
Monthly payment = Remaining balance / Number of months
Monthly payment = $20,700 / 24
Monthly payment ≈ $862.50
Therefore, the size of each monthly payment is approximately $862.50.