Question

A loan of $4500 was received on January 1, 2011. Quarterly payments to settle the debt begin on April 1, 2014 and end on October 1, 2018. If the interest rate on the loan was 8% compounded quarterly, determine the size of the payments. ($364.01) Cannot use Excel.

Answer 1

Value of loan on January 1, 2014 = Value of loan on January 1, 2011 * (1 + r)ⁿ

= $4500 * [1 + (0.08/2)]^(3*4)

= $4500 * 1.2682 = $5707.09

No. of Payments = payments in 2014 + payments in 2015 + payments in 2016 + payments in 2017 + payments in 2018

= 3 + 4 + 4 + 4 + 4 = 19

As the first payment is to be made after the end of 3 months. So, this is an example of ordinary annuity.

So, Quarterly Payment = [Value of loan on January 1, 2014 * r] / [1 - (1 + r)^-n]

= [$5707.09 * (0.08/4)] / [1 - {1 + (0.08/4)}^-19]

= $114.14 / 0.3136 = $364.01