john borrowed $650 from credit union . interest rate is 7.9% , and takes loan for 6 months . what will be his monthly payment to repay loan plus interest ?
If this is simple interest then the interest in 1/2 a year would be
(1/2)(.079)(650) = 25.675
(650 + 25.675)/6 = 112.61
If this is some kind of compounded or declining balance (mortgage) type loan then you have not provided enough information.
112.61
To calculate John's monthly payment to repay the loan plus interest, we need to use the formula for calculating the monthly payment on a loan:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Total Number of Payments))
First, let's determine the values needed to plug into the formula:
Loan Amount = $650
Interest Rate = 7.9% per year
Number of Payments = 6 months
To calculate the monthly interest rate, we need to convert the annual interest rate to a monthly rate. Since we have a 7.9% annual interest rate, we divide it by 100 (to convert it to decimal form) and then divide by 12 (to get the monthly rate):
Monthly Interest Rate = (7.9 / 100) / 12 = 0.00658 (rounded to 5 decimal places)
Plugging the values into the formula:
Monthly Payment = (650 * 0.00658) / (1 - (1 + 0.00658)^(-6))
Next, we simplify the formula:
Monthly Payment = (650 * 0.00658) / (1 - (1.00658)^(-6))
Calculating the exponent:
(1.00658)^(-6) ≈ 0.9939 (rounded to 4 decimal places)
Now, we can substitute this value back into the formula:
Monthly Payment = (650 * 0.00658) / (1 - 0.9939)
= 4.27 / (1 - 0.9939)
= 4.27 / 0.0061
Finally, we calculate the monthly payment:
Monthly Payment ≈ $700.40 (rounded to 2 decimal places)
Therefore, John's monthly payment to repay the loan plus interest would be approximately $700.40.