Answered

You deposit $10,00 into an investment account that results in your money earning 5.2% interest compounded monthly. a) determine the value of the account after 10 years.B) How many years will it take for it to triple.

Answer :

Solution

Part a

We can do the following:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

For this case we can replace and we have:

[tex]A=10000(1+\frac{0.052}{12})^{12\cdot10}=16801.39[/tex]

Part b

For this case we can do the following:

[tex]30000=10000(1+\frac{0.052}{12})^{12\cdot t}[/tex]

Solving for t we have

[tex]3=(1+\frac{0.052}{12})^{12t}[/tex][tex]\ln (3)=12t\ln (1+\frac{0.052}{12})[/tex][tex]t=\frac{\ln (3)}{12\cdot\ln (1+\frac{0.052}{12})}=21.17[/tex]

then the answer is 21.1 years

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