Compound Interest

**magentarita** · August 11th 2008, 04:51 AM

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?

**Simplicity** · August 11th 2008, 05:17 AM

Originally Posted by magentarita

If Angela has $100 to invest at 10% per annum compounded monthly, how long will it be before she has $175?

The compound interest formula is:

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

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

From the question, we can deduce that P=$100, r=0.1, n=12, t=?, A=$175 and hence inserting the values into the formula gives:

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

Now, solve for $t$ and you will have the amount of years for the investment to grow from $100 to $175.

**Simplicity** · August 11th 2008, 05:24 AM

Originally Posted by magentarita

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?

The continuous compound interest formula is:

$A = Pe^{rt}$

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:

$175 = 100e^{0.1t}$

Now, solve for $t$ and you will have the amount of years for the investment to grow from $100 to $175 with continuous compound interest.

**magentarita** · August 11th 2008, 09:04 PM

Great reply as always!

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