Brian borrowed $400 for 1 year. His payments are $34.50 a month. If he decides to pay the loan off after 8 months, find the amount of interest that he will save.
P = Po + Po*r*T = 34.50*12,
400 + 400*r*1 = 414,
r = 0.035 = 3.5%. = APR.
414 - 400 = $14. = Int. after one yr.
I = Po*r*T = 400*0.035*(8/12) = $9.33 = Int. after 8 months.
14 - 9.33 = $ __ = Int. saved.
To find the amount of interest that Brian will save by paying off the loan after 8 months, we need to calculate the total interest paid for the full one year and then subtract the interest paid for the 8-month period.
First, let's find the total interest paid for the loan over one year.
The total amount borrowed is $400, and the loan term is 1 year.
The formula to calculate the total interest is:
Total Interest = (Loan Amount) x (Annual Interest Rate) x (Loan Term in years)
However, we don't have the annual interest rate. Instead, we know the monthly payments and repayment term. So let's find the annual interest rate using the given information.
Brian is making monthly payments of $34.50, and he is repaying the loan over 1 year, which is 12 months.
The formula to calculate the annual interest rate is:
Annual Interest Rate = (Monthly Payment / Loan Amount) x (12 / Loan Term in months)
Annual Interest Rate = ($34.50 / $400) x (12 / 12)
Annual Interest Rate = 0.08625 or 8.625%
Now that we have the annual interest rate, we can calculate the total interest paid over one year.
Total Interest = $400 x 0.08625 x 1
Total Interest = $34.50
Therefore, the total interest paid for one year is $34.50.
To find the interest saved by paying off the loan after 8 months, we can calculate the interest paid for 8 months using the same formula, considering the loan term is now 8 months.
Interest Paid for 8 months = (Loan Amount) x (Annual Interest Rate) x (Loan Term in years)
Interest Paid for 8 months = $400 x 0.08625 x (8 / 12)
Interest Paid for 8 months = $22.50
Therefore, by paying off the loan after 8 months, Brian will save $22.50 in interest.