Question 1109990: Joe secured a loan of $13,000 five years ago from a bank for use toward his college expenses. The bank charges interest at the rate of 3%/year compounded monthly on his loan. Now that he has graduated from college, Joe wishes to repay the loan by amortizing it through monthly payments over 12 years at the same interest rate. Find the size of the monthly payments he will be required to make.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the original loan was for 13,000 at 3% per year compounded monthly.
he has presumably not paid any part of the loan off until he graduated from college.
presuming that it took him 4 years to complete college, then the value of the loan was 13,000 * (1 + .03/12) ^ (4*12) = 14655.26427 when he graduated.
he wants to pay this loan off in 12 years at the same interest rate.
assuming you can use a financial calculator, like the TI-BA-II, you would make the following entries.
present value = 14655.26427.
future value = 0
interest rate per month = 3/12
number of months = 12 * 12
payments are made at the end of each month.
you would then solve for monthly payments to get:
monthly payments = 121.3143269 per month.
--------------------------------------------------------------
the future value of a present amount formula is:
f = p * (1 + r) ^ n
f is the future value
p is the present value
r is the interest rate per time period.
n is the number of time periods.
there are 12 compounding periods per year.
you time periods are months.
your interest rate per year is .03
divide that by 12 to get .03/12 is your interest rate per month.
your number of years is 4.
multiply that by 12 to get 4 * 12 months.
i used a calculator to get your monthly payments, but you can do that by formula as well.
the formula to use is:
ANNUITY FOR A PRESENT AMOUNT WITH END OF TIME PERIOD PAYMENTS
a = (p*r)/(1-(1/(1+r)^n))
a is the annuity.
p is the present amount.
r is the interest rate per time period.
n is the number of time periods.
------------------------------------------------
in this formula, replace p with 14655.26427 and replace r with .03/12 and replace n with (12*12).
the formula becomes:
a = (p*r)/(1-(1/(1+r)^n))
a = (14655.26427*.03/12)/(1-(1/(1+.03/12)^(12*12)))
solve for a to get:
a = 121.3143269.
this is the same value as the result that the calculator gave you.
when using the calculator, percent is used.
when using the formula, rate is used.
rate = percent / 100.
3% = .03
your solution is that the monthly payments required to make are 121.3143269.
|
|
|
