SOLUTION: A loan of $ 10500 is to be repaid in 43 equal monthly installments with the first one paid seven months after the loan is made. The nominal annual interest rate is 13 % compounded
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Question 1192613: A loan of $ 10500 is to be repaid in 43 equal monthly installments with the first one paid seven months after the loan is made. The nominal annual interest rate is 13 % compounded semiannually. Determine the amount of the monthly payment.
You can put this solution on YOUR website! the loan amoun is 10,500.
the interest rate is 13% compounded semi-annually.
the loan needs to be paid in 43 equal monthly installments.
the first payment will be made 7 months after the loan is made.
the semi-annual interest rate is 13/2 = 6.5%.
the monthly growth rate is (1.065)^(1/6) = 1.010551074.
if you take 1.010551074 and raise it to the 6th power, you will get the semi-annual growth rate of 1.065.
the semi-annual growth rate of 1.065 minus 1, times 100 = the semi-annual interest rate of 6.5%.
the effective annual growth rate is 1.065 ^ 2 = 1.134225.
it is also 1.010551075 ^ 12 = 1.134225.
the effective annual interest rate is 1.134225 minus 1, times 100 = 13.4225%.
now that we have the monthly growth rate, we can solve the problem.
for the first 6 months, nothing is paid, but the interest is applied to raise the principal from 10500 to 10500 * 1.010551075 ^ 6 = 11182.5.
that becomes the present value of the 43 month annuity where the payments are equal.
you can use a formula, or you can use a calculator.
the calculator i used is the ti-ba-ii business analyst by texas instruments.
my inputs to that calculator were:
present value = 11182.5
future value = 0
number of time periods = 43 months.
interest rate per time period = 1.055107398%
payments made at the end of each time period.
i then had the calculator tell me what the monthly payments were.
it said the payments made at the end of each month were equal to 324.8438861.
round to the nearest penny to get $324.84.
that should be your answer.
i put the problem in excel to show the monthly transactions and also to confirm the calculations were correct.
this is what excel showed.
excel confirms that the calculations were correct, based on the assumptions that i used.
