Question

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.

Answer 1

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