Financial Mathematics → Interest → Simple Interest → Compound Interest → Continuous Interest → Accumulation Factor

In Interest for different compounding periods, we have the formula for accumulated amount

Where is called accumulation factor.

So, an investment for a term h from time t to time t+h has accumulation factor

Where,

is called effective rate of interest per annum, and

is called nominal rate of interest per annum.

If we take the initial time and the final time , then the formula for accumulation factor has become

So, the formula

can also be written as

because

because

**Example 1.** Let time be measured in years. Find the accumulation after 12 years of an investment of $1500 made at any time, if the accumulation factor is

**Solution:**

As we know that the accumulation