# Math Help - Compound Interest

1. ## 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?

2. 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.

3. 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.