Exercise 6-16 Deferred annuities; solving for annuity amount LO6-7,6-8] On April

Question

Exercise 6-16 Deferred annuities; solving for annuity amount LO6-7,6-8] On April 1, 2016, John Vaughn purchased appliances from the Acme Appliance Company for $1,300. In order to increase sales, Acme allows customers to pay in installments and will defer any payments for six months. John will make 18 equal monthly payments, beginning October 1, 2016. The annual interest rate implicit in this agreement is 24%. (EV of $1 PV of $1. $1) (Use appropriate factor(s) from the tables provided.) EVA of $1. PVA of $1. EVAD of $1 and PVAD of Required: Calculate the monthly payment necessary for John to pay for his purchases. Monthly payment

Explanation / Answer

This question can be solved by calculating the present value of deferred annuity on October 1, 2016 and then calculating its present value on April 1,2016

The present value of annuity = P*(1 - (1+r)^-n)/r

Where P= annuity payments

R = 24/12 = 2%

N = 18

Present value of annuity on April 1 = (P*(1-(1.02)^-18)/0.02)/((1+0.02)^6))

= 13.31*P

So,

13.31*P = 1300

P = 97.67

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