Question

Evan took a loan of $7,600 from her parents to purchase equipment for her hair salon. They agreed on an interest rate of 3% compounded monthly on the loan. What equal quarterly payments made at the end of each period will settle the loan for 5 years if the first payment is to be made 3 years and 1 quarter from now?

Answer 1

Loan amount	7600
Interest rate	3%
Quarterly rate	0.75%
1st payment	3years 1 quarter
1st payment (in quarters)	13
Last payment (in years)	5
Last payment (in months)	20

Present value of annuity = quarterly payment x (((1-(1+quarterly rate)^-20)/quarterly rate) - ((1-(1+quarterly rate)^-12)/quarterly rate))

Present value of annuity = quarterly payment x (((1-(1+0.75%)^-20)/0.75%) - ((1-(1+0.75%)^-12)/0.75%))

Present value of annuity = quarterly payment x (18.51 - 11.43)

7600 = quarterly payment x (7.07)

7600 / 7.07 = quarterly payment

Quarterly payment = $ 1075

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