To determine the nominal interest rate, we need to use the formula for the future value of an annuity:
\[FV = P \times \left(1 + \frac{r}{n}\right)^{nt} - P\]
Where:
FV = Future value of the annuity (K7500)
P = Quarterly payment (K500)
r = nominal interest rate
n = number of compounding periods per year (4 for quarterly compounding)
t = number of years (3 years)
Substitute the values into the formula:
\[7500 = 500 \times \left(1 + \frac{r}{4}\right)^{4*3} - 500\]
Simplify the equation:
\[7500 = 500 \times \left(1 + \frac{r}{4}\right)^{12} - 500\]
\[8000 = \left(1 + \frac{r}{4}\right)^{12}\]
Taking the 12th root of both sides:
\[1 + \frac{r}{4} = \sqrt[12]{8000}\]
\[1 + \frac{r}{4} \approx 1.1089\]
\[\frac{r}{4} \approx 0.1089\]
\[r \approx 0.4356\]
Therefore, the nominal interest rate is approximately 43.56%.
At the end of each quarter a payment of K500 is made into an account which bearing interest compounded quarterly. If the annuity accrues to K7500 over three years, determined the nominal interest rate.
1 answer
1 answer