compound interest problem

Aug 2017
91
1
England
can some one please help me with this question

A sum of $300.24 is paid into a loan account at the end of every month for 5 years. Calculate the present value of the payments if interest is calculated on the basis of 7.5% per annum convertible quarterly.



The answer is $15,000.
 
Feb 2015
2,255
510
Ottawa Ontario
A sum of 300.24 is paid into a loan account at the end of every month for 5 years.
Calculate the present value of the payments if interest is calculated on the basis of 7.5% per annum convertible quarterly.
The answer is 15,000.
7.5% per annum convertible quarterly =
(1 + .075/4)^4 - 1 = .077136, so ~7.7136% effective per annum.

Formula to calculate PV of annuity: PV = p[1 - 1/(1 + i)^n] / i
p = 300.24
n = 5*12 = 60
i = .077136/12
That'll give PV = 14907.94

So (unless I goofed) there's something wrong with the problem as posted
You sure 300.24 is correct?
302 gives ~14,995
303 gives ~15,044
Perhaps the 300.24 should be 302.40: then all would be fine!!