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Question

# This exercise concerns a single investment of $10,000. Find the continuous interest rate per year, yielding a future value of$20,000 in the given time period. 60 years

Solution

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Consider Present value is $10,000$ and future value is $20,000$ in 60 years then the future value is

$B=P e^{rt}$

Here $B$ is future value and $P$ is present Value

Consider a single deposit of $\10000$ and future value of $\20000$ in 60 year time period.

\begin{align*} 20000 &=10000 e^{r(60)} \\ 2 &=e^{r(60)} \end{align*}

\begin{align*} \ln 2 &=\ln e^{r(\infty)} \\ \ln 2 &=r 60 \\ \frac{\ln 2}{60} &=r \\ r &=0.0115 \end{align*}

\begin{align*} r &=0.0115 \times 100 \\ &=1.15 \% \end{align*}

Thus the interest rate $1.15 \%$ which yields a future value of $20,000$ in time period of 60 years

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