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SpyIntel [72]
3 years ago
5

find the value of an investment of $3500 for 3 years at an interest rate of 5.6% if the money is compounded weekly

Mathematics
1 answer:
sergeinik [125]3 years ago
3 0
\bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to &\$3500\\
r=rate\to 5.6\%\to \frac{5.6}{100}\to &0.056\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{weekly, thus fifty two}
\end{array}\to &52\\
t=years\to &3
\end{cases}

\bf A=3500\left(1+\frac{0.056}{52}\right)^{52\cdot 3}\implies A=3500\left( \frac{6507}{6500} \right)^{156}
\\\\\\
A\approx 4139.9038869337
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Given parameters;

  Let us solve this problem step by step;

Let us represent Simon's money by S

Kande's money by K

  • Simon has more money than Kande

               S > K

  •  if Simon gave Kande K20, they would have the same amount;

 if Simon gives $20, his money will be  S - 20 lesser;

      When Kande receives $20, his money will increase to K + 20

                     S - 20  = K + 20   ------ (i)

  • While if Kande gave Simon $22, Simon would then have twice as much as Kande;

          if Kande gave Simon $22, his money will be K - 22

    Simon's money, S + 22;

                  S + 22  = 2(K - 22)    ------ (ii)

Now we have set up two equations, let us solve;

         S - 20  = K + 20  ---- i

         S + 22  = 2(K - 22)  ;       S + 22  = 2K - 44  ---- ii

So,      S - 20  = K + 20

          S + 22  = 2K - 44

subtract both equations;

               -20 - 22  = (k -2k)  + 64

                   -42  = -k + 64

                       k  = 106

Using equation i, let us find S;

            S - 20 = K + 20

             S - 20  = 106 + 20

              S = 106 + 20 + 20  = 146

Therefore, Kande has $106 and Simon has $146

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