## Related questions with answers

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. 5 years

Solution

VerifiedConsider Present value is $10,000$ and future value is $20,000$ in 15 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.

$\begin{align*} 20000 &=10000 e^{r(5)} \\ 2 &=e^{r(5)} \end{align*}$

$\begin{align*} \ln 2 &=\ln e^{r(s)} \\ \ln 2 &=r \times 5 \\ \frac{\ln 2}{5} &=r \\ r &=0.1386 \end{align*}$

$\begin{align*} r &=0.1386 \times 100 \\ &=13.86 \% \end{align*}$

Thus the interest rate $13.86 \%$ which yields a future value of $20,000$ in time period of 5 years

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