Question

A fund of $24000 is to be accumulated by n quarterly payments of $2800 where the n^th payment is a larger payment which brings the fund to $24000. If interest is at j₄= 9%, determine n and the final irregular payment.

Answer 1

According to the question, we need n payments of $2800 and one payment bigger than $2800 to make the fund to $28,000. The future value equation will look like:

24,000 = 2800 x (1.09^2 + 1.09^3 + ... + 1.09^n)

We have started the formula with t=2 because the last bigger payment will grow for 1 year and the secon-last payment of $2800 will grow for 2 years and so on. Hence, by hit-and-trial, we find that n = 6. So, the 6th payment will be the irregular payment. The fund value because of these 5 payments will become = 2800 x (1.09^6 + 1.09^5 + 1.09^4 + 1.09^3 + 1.09^2) = 19909.217. Hence, the remaining amount is = 24000 - 19909.217 =4090.783 . This is the amount we need to make the fund reach $24,000. Hence, the 6th payment will be = 4090.783/1.09 = 3753.0119.

Hence, n = 6 and irregular payment is $3,753.0119