A property was purchased for ?$7640.00 down and payments of ?$867.00 at the end of every six months for 10 years. Interest is 6% per annum compounded quarterly. What was the purchase price of the? property? How much is the cost of? financing?

 

Purchase price of property = $20,457.84

Cost of financing = $4,522.16

Step-by-step explanation

Computation of the purchase price of property:-

First we calculate the present value of annuity ;

PV of annuity = Annuity*((1-1/(1+rate)^n)/rate)

Here, rate = 6.14% / 2 = 3.07% (semiannual)

n = 10*2 20 periods (semiannual)

PV of annuity = $867*((1-1/(1+3.07%)^20)/3.07%

= $867*14.7841

= $12,817.84

Purchase price = Down payment + PV of annuity

= $7,640 + $12,817.84

= $20,457.84

Working note:-

EAR = (1+rate/n)^n-1

= (1+6%/4)^4-1

= 1.0614 - 1

= 6.14%

Computation of the cost of financing:-

Cost of financing = Total payment - PV of annuity

= ($867*10*2) - $12,817.84

= $17,340 - $12,817.84

= $4,522.16