Question

For an investment, $25 000 is deposited into an account. The interest rate is 8% per annum, compounded annually, with annual payments starting in a year. How much is each payment?

The textbook did not provide the value of n. This was part of a series of questions with the compounding periods changing to semi-annually, quarterly, and then monthly for the next three problems. The purpose of the problem set was to determine what happens to payments as the compounding period decreases, but I don't understand how!!!

Answer 1

Ok, let's understand how changing the compounding period affects the payments we make.

Let's assume the value of n is 10.

1) 8% per annum compounded annually

PV = 25,000

2) Now let's increase the compounding frequency: 8% per annum compounded semi-annually

If we keep n = 10, then the effective annual rate = (1 + 0.08/2)^2 - 1 = 0.0816

(Note that to know the effect of only the compounding frequency, we should keep everything else constant. So, n = 10)

Note that with increase in compounding frequency we get more in interest from the same deposit of $25,000