Nathan would like to have $15000 in 10 years, and can afford to deposit $500 every 6 months in an investment account. What interest rate, compounded semi-annually, does he need to achieve his goal? Show step by step.

The semi-annual deposit is $500

The number of deposits in 10 years is 20

The needed amount by the end of 10 years is $1500

The formula to use is

A = F i / [ (i + 1) ^n - 1]

500 = 1500 i / ] (1 + i) ^20 - 1]

Solve for i and this will give you the effective interest rate compounded semi-annually

Solve for the nominal interest rate using

(1 + i) ^2 = (1 + i_nom) ^6

Then, solve for i_nom