## 2.4 Predicting Future Values for Compound Interest Loans and Investments

### Predicting Future Values involving Compound Interest

- Predicting the value of a compound interest system after a large number of compounding periods is a long and tedious process using recursion. Fortunately, for systems which
**do not involve regular additions or withdrawals**, we can use the convenient formula:

A_{n}=\left(1+\frac{r}{100}\right)^{n} A_{0}

Where A_{n} is the amount after n compounding periods, r is the interest as a percentage and A_{0} is the initial value.

- When dealing with systems which
**do have regular additions or withdrawals**, the only method we have (in the scope of this course) is recursion.