If Angela has $100 to invest at 10%per annumcompounded monthly, how long will it be before she has $175? If the compounding is continuous, how long will it be?

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- Aug 11th 2008, 04:51 AMmagentaritaCompound Interest
If Angela has $100 to invest at 10%

**per annum**compounded monthly, how long will it be before she has $175? If the compounding is continuous, how long will it be? - Aug 11th 2008, 05:17 AMSimplicity
The compound interest formula is:

$\displaystyle A = P\left(1 + \frac{r}{n}\right)^{nt}$

Where:

- P = Principal amount (initial investment)
- r = Annual interest rate (as a decimal)
- n = Number of times the interest is compounded per year
- t = Number of years
- A = Amount after time t

$\displaystyle 175= 100\left(1 + \frac{0.1}{12}\right)^{12t}$

Now, solve for $\displaystyle t$ and you will have the amount of years for the investment to grow from $100 to $175. - Aug 11th 2008, 05:24 AMSimplicity
The continuous compound interest formula is:

$\displaystyle A = Pe^{rt}$

Where:

- P = Principal amount (initial investment)
- r = Annual interest rate (as a decimal)
- t = Number of years
- A = Amount after time t
- e = Exponential function

From the question, we can deduce that P=$100, r=0.1, t=?, A=$175 and hence inserting the values into the formula gives:

$\displaystyle 175 = 100e^{0.1t}$

Now, solve for $\displaystyle t$ and you will have the amount of years for the investment to grow from $100 to $175 with continuous compound interest. - Aug 11th 2008, 09:04 PMmagentaritaGreat reply...
Great reply as always!