SOLUTION: A business borrowed 50000 at 8% compounded monthly. If the loan is to be paid in equal quartely payments over seven years and the first payment in due three months after the date o

Question 1149835: A business borrowed 50000 at 8% compounded monthly. If the loan is to be paid in equal quartely payments over seven years and the first payment in due three months after the date of the loan, calculate the size of the quartely payments.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
present value = 50,000
interest rate = 8% per year / 12 = (2/3)% per month.
loan is to be paid quarterly.
3 months at (2/3)% per month = 2.013362963% per quarter.
payments at the end of each quarter are $2,353.553011.
round to nearest penny and they are $2,353.55.

since the interest is compounded monthly, then the monthly interest rate is equal to ((1 + .08/12) - 1) * 100 = .6666666667% per month.

the 8% per year is your nominal interest rate per year.
.66666666667% per month is your effective interest rate per month.

your effective interest rate per quarter is ((1 + .08/12)^3 - 1) = 2.013362963% per quarter.

your quarterly payment is calculated using the effective interest rate per quarter as shown in the following online financial calculator display.

the present value is shown as positive because it's what you received.
the payment is shown as negative because it's what you payed out.

here's the display of the online calculator results.

$$$

here's a display of the excel analysis that confirms the solution is correct as best i can determine.

$$$

for use in the calculator, the quarterly interest rate was calculated as follows:

quarterly interest rate % = ((1 + .08/12) ^ 3 - 1) * 100 = 2.013362963

for use in the excel printout, the monthly interest rate was calculated as follows:

monthly interest rate = ((1 + .08/12)) - 1 = .0066666666667

the calculate used the interest rate percent.
the excel used the interest rate.
percent = rate * 100
rate = percent / 100

i have no time for further explanation.
if you have questions, email to dtheophilis@gmail.com and i'll answer as soon as i can - probably by tomorrow morning the latest.

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