|
Question 1140258: How long (in years) will it take Michael Garbin to pay off a $3000 loan with monthly payments of $154.95 if the add-on interest rate is 7.8%?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! an add-on interest type loan adds the interest up front to the principal and then both the principal and the interest have to be payed off.
in your loan.
the principal is 3000
the yearly interest rate is .078
the monthly interest rate is .078 / 12 = .0065
looking at the possible number of month for your loan, assuming the loan is for a specified number of months, i don't get any number of months for the loan that would result in a payment of 154.95 a month.
the closest i get is for a 22 month loan.
my calculations for that loan would be:
3000 + .0065 * 3000 * 22 = 3429 / 22 = 155.8636364 per month.
that says that the number of months has to be between 22 and 23, based on your monthly payment figures.
i'm assuming, of course, that the payment per month would be the payment for the principal of 3000 plus the interest on that principal since that is how add-on interest loans are paid off.
this tells me that the 154.95 per month is to pay off the principal plus the interest for the number of months of the loan.
i then looked to derive a formula to determine the exact number of months required to pay off the loan.
my formula was:
n = 3000 / (mp - .0065 * 3000).
n represents the number of months required to pay off the loan.
mp equals the monthly payment.
i then checked this out for loans that i knew the number of months and the monthly payment for.
for example, on a 24 month loan, the monthly payment would be 144.5.
based on that the formula becomes:
n = 3000 / (144.5 - .0065 * 3000) = 24
this told me the formula is accurate and will help me to determine the exact number of months for your loan.
since your monthly payment is 154.95, the formula becomes:
n = 3000 / (154.95 - .0065 * 3000) = 22.14839424
that tells me that the number of months required to repay your loan with a payment of 154.95 per month would be equal to 22.14839424.
since 22.14849424 months is between 22 and 23, that checks out with my previous analysis that assumed it has to be between 22 and 23 months.
22.14839424 months / 12 = 1.84569952 years.
that says that the number of years to required pay off your loan is equal to 1.84569952 years, based on a payment of 154.95 per month.
i don't know where the 154.95 came from, but using that value as the monthly payment does not allow me to come up with a number of months that is an integer.
here's a link to an add-on interest loan calculator that you might find useful.
http://www.csgnetwork.com/addonintcalc.html
here's a reference on add-on interest type loans.
https://www.investopedia.com/terms/a/add-on_interest.asp
|
|
|
| |
