Question

8. How much would you need to deposit in an account earning 5.6% compounded weekly in order to have $3,960 in the account in 10 years?$

Answer 1

In order to calculate the initial value, let's use the formula for compound interest:

$P=P_0\cdot(1+\frac{i}{n})^{nt}_{}$

Where P is the final amount after t years, P0 is the initial amount, i is the annual interest and n is how many times the interest is compounded in a year.

So, using P = 3960, i = 0.056, t = 10 and n = 52 (there are 52 weeks in a year), we have:

$\begin{gathered} 3960=P_0\cdot(1+\frac{0.056}{52})^{52\cdot10} \\ 3960=P_0\cdot1.750145 \\ P_0=\frac{3960}{1.750145}=2262.67 \end{gathered}$

So you need to deposit $2262.67.