Question

I want to buy a boat today today but have realised that if I take out a loan I can only repay $150 quarterly, with payments made at the beginning of each quarter, over the next 5 years. How much can I spend on my boat if the interest rate is 16% per annum compounded quarterly ?

A. $2,120.09

B. $4,020.04

C. $4,466.71

D. $2,038.55

Answer 1

Since payments are to be made at the beginning of each quarter, we will calculate the present value of all the instalments leaving the 1st instalment using present value annuity factor. and then add the 1st instalment amount as it stands at year zero

Time = 19 quarters

Interest = 4%

PVAF 19,4 = 13.1339394

Therefore present value of all the instalments is equal to

150 + (13.1339 x 150) = 2120.09

So the correct answer is option A

Note : This question is of annuity due, kindly go through the concept of annuity due for further clarity