Question

You deposit $10,00 into an investment account that results in your money earning 5.2% interest compounded monthly. a)How many years will it take for you to have 100,000$ in the account? Answer to the nearest 100th of a year. B) what interest rate would be required to have $100,000 in the account? Answer to the nearest 100th of a year. Changes:you deposit $10,000^ i made a mistake in thew questionB.what interest rate would be required to have $100,000 in the account after 25 years? Answer to the nearest 100th of a year.

Answer 1

Given:

$P=\text{ \ 10,000 ; }r=0.052$

a)

A= $100,000

$A=P(1+\frac{r}{12})^{12t}$$\begin{gathered} 100000=10000(1+\frac{0.052}{12})^{12t} \\ \frac{100000}{10000}=(\frac{12.052}{12})^{12t} \\ 10=(1.0043)^{12t} \\ 10=(1.0533)^t \\ t=44.38 \end{gathered}$

It takes 44.38 years to have $100,000 in the account.

b)

A=$100,000 ; t=25

$\begin{gathered} 100000=10000(1+\frac{r}{12})^{12(25)} \\ 10=(\frac{12+r}{12})^{300} \\ r=0.0925 \end{gathered}$

Interest rate is 9.25% per year.