question archive A property was purchased for ?$7640
Subject:FinancePrice:2.86 Bought5
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