Question

you invested $9000 at the end of each half year for 6 years in an investment fund. At the end of year 6, if the balance in the fund was $ 121,000 what was the nominal interest rate compounded semi annually?

Answer 1

To find the nominal interest rate compounded semi-annually, we can use the formula for compound interest. Substituting the known values, we find that the nominal interest rate is approximately 4.5%.

Step-by-step explanation:

To find the nominal interest rate compounded semi-annually, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the balance in the fund at the end of year 6 ($121,000)
P = the initial investment amount ($9,000)
r = the nominal interest rate we want to find
n = the number of compounding periods per year (2 for semi-annually)
t = the number of years (6)

Substituting the known values into the formula, we have:

$121,000 = $9,000(1 + r/2)^(2 * 6)

Simplifying the equation, we get:

13.444 = (1 + r/2)^12

Using trial and error or an iterative method, we find that the nominal interest rate r is approximately 0.045 or 4.5%.