Question

K7000 is paid at the end of each quarter into an account which bearing interest compounded quarterly. If the annuity accrues to K10000 over five years, determine the nominal interest rate

Answer 1

To determine the nominal interest rate, we will use the formula for the future value of an annuity:

FV = P * ((1 + r)^n - 1) / r

Where:
FV = future value of the annuity (K10000)
P = periodic payment (K7000)
r = nominal interest rate per quarter
n = number of periods (5 years * 4 quarters per year = 20 quarters)

Substitute the given values into the formula:

10000 = 7000 * ((1 + r)^20 - 1) / r

Now we need to solve for the nominal interest rate 'r'. This equation doesn't have a direct solution, so we will need to use numerical methods or trial and error to find the value of 'r'.

Using a financial calculator or a spreadsheet software, we can plug in different values for 'r' until we find the one that makes the equation true. This process might be a bit tedious, but it will give us the nominal interest rate that satisfies the equation.

The nominal interest rate can also be estimated by assuming an interest rate, plugging it into the formula, and adjusting the rate until the future value is closest to K10000.