Question

find the number of years required to reach the intended future value at the given rate: p=$7000, FV=$10000, r=4.3%

Answer 1

Given :

p =$7000,

A = $10000,

r = 4.3% = 0.043

Assume a simple interest

`\begin{gathered} A=P+I \\ I=P\cdot r\cdot t \\ A=P+P\cdot r\cdot t \\ A=P\cdot(1+r\cdot t) \end{gathered}`

So,

`\begin{gathered} A=P\cdot(1+r\cdot t) \\ 10000=7000\cdot(1+0.043\cdot t) \end{gathered}`

Solve for t :

`\begin{gathered} 10000=7000\cdot(1+0.043\cdot t) \\ 1+0.043\cdot t=(10000)/(7000)=(10)/(7) \\ 0.043\cdot t=(10)/(7)-1 \\ \\ 0.043t=0.42857 \\ \\ t=(0.42857)/(0.043)\approx9.97 \end{gathered}`

So, rounding to the nearest year

So, time = 10 years

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