Question

A vacation property valued at

$65,000

was bought for

120

payments of

$ 1555

due at the end of every

3 months.

What nominal annual rate of interest compounded

semi-annually

was charged?

Answer 1

Property Price = $ 65000, Repaymentse = $ 1555 , Number of Payments = 120, Payment Frequency = Quarterly, Compounding Frequency: Semi-Annual

Let the applicable quarterly rate be r %

Therefore, 65000 = Total Present Value of the Quarterly Payments = 1555 x (1/r) x [1-{1/(1+r)^(120)}]

Using EXCEL's Goal Seek Function to solve the above equation, we get:

r = 0.02221 or 2.221 %

As compounding is done semi-annually and one semi-annual period has two quarters, the equivalent semi-annual rate = (1.02221)^(2) - 1 = 0.04491 or 4.491 %

Nominal Annual Rate = 2 x Equivalent Semi-Annual Rate = 2 x 4.491 = 8.982 % ~ 8.98 %