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 compound interest formula is:
$\displaystyle A = P\left(1 + \frac{r}{n}\right)^{nt}$
Where:
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:
- 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.
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.