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

User Ueeieiie
by
3.2k points

1 Answer

9 votes
9 votes

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.

User Ketsy
by
2.3k points
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