Question

Olanda needs for a future project. She can invest now at an annual rate of , compounded monthly. Assuming that no withdrawals are made, how long will it take for her to have enough money for her project?

Answer 1

Answer:

$t=\frac{ln[\frac{A}{x}]}{n*ln[1+\frac{R}{n}]}$

Step-by-step explanation:

As the question is not complete, we will generalize the statement as follows:

Olanda needs "A" for a future project. She can invest "x" now at an annual rate of "R" , compounded monthly. Assuming that no withdrawals are made, how long will it take for her to have enough money for her project?

A= Amount Olanda needs (future value).

X= Amount available for Olanda.

R= Anual rate.

First, we have that the future value is given by:

$A=x(1+\frac{R}{n}) ^{nt}$

Where n=12 because the rate is annual.

And we need to calculate the time it will take with that annual rate to get the money she needs (future value) from what she has now (present value). So, we must make it explicit for "t"; solving:

We have:

$\frac{A}{x} = (1+ \frac{R}{n})^{nt}$

$ln[\frac{A}{x}]=ln[ (1+ \frac{R}{n})^{nt}]$

Applying logarithmic properties

$ln[\frac{A}{x}]=nt*ln[1+\frac{R}{n}]$

Finally, we have:

$t=\frac{ln[\frac{A}{x}]}{n*ln[1+\frac{R}{n}]}$