# Compound Interest

• Aug 11th 2008, 04:51 AM
magentarita
Compound 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 AM
Simplicity
Quote:

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:

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

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
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:

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

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 AM
Simplicity
Quote:

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:

$\displaystyle A = Pe^{rt}$

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 PM
magentarita