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Question 1104295: Jason received a loan of $9,000 at 6.75% compounded quarterly. He had to make payments at the end of every quarter for a period of 1 year to settle the loan
Calcu.ate the size of payments?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the loan was 6000 at 6.75% compounded quarterly.
he had to make payments at the end of each quarter for a period of 1 year.
present value = 6000
future value = 0
r% = 6.75% / 4= 1.6875% per quarter.
number of quarters = 1 year * 4 = 4 quarters.
payment made at the end of each quarter.
using a financial calculator, the payments would need to be equal to 1563.810689 at the end of each quarter.
at the beginning of the year, the remaining balance of the loan is 6000.
at the end of the first quarter, the remaining balance of the loan would be equal to 6000 * (1 + .0675/4) - 1563.810689 = 4537.439311.
at the end of the second quarter, the remaining balance of the loan would be equal to 4537.439311 * (1 + .0675/4) - 1563.810689 = 3050.197911.
at the end of the third quarter, the remaining balance of the loan would be equal to 3050.197911 * (1 + .0675/4) - 1563.810689 = 1537.859313.
at the end of the fourth quarter, the remaining balance of the loan would be equal to 1537.859313 * (1 + .0675/4) - 1563.810689 = 0.
the calculators usually work on percent, while the manual formulas usually work on the rate, which is the percent divided by 100.
if you need the manual formula to calculate the payment, that formula would be as shown below:
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.
annuity and payment mean the same thing for this formula.
in your problem, the formula becomes a = (6000 * .0675/4) / (1 - (1 / (1 + .0675/4) ^ 4))
put the expression in your calculator exactly as shown and you get a = 1563.810689.
this is the same as the solution that the calculator gave me.
the calculator i used is the TI-BA Plus.
BA stands for business analyst.
other financial formula you might find useful can be found here:
https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#f9
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