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+(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+(0.056)/(52))^(52\cdot10) \\ 3960=P_0\cdot1.750145 \\ P_0=(3960)/(1.750145)=2262.67 \end{gathered}`

So you need to deposit $2262.67.