Accumulation Factor

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 1+hi_h(t) is called accumulation factor.

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

A(t,t+h) = 1 + hi_h(t)


hi_h(t) = A(t,t+h) - 1

is called effective rate of interest per annum, and

is called nominal rate of interest per annum.

Accumulation Factor Chart

If we take the initial time t = t_1 and the final time t+h = t_2  , then the formula for accumulation factor has become

So, the formula

can also be written as

A = CA(t,t+h) because A(t,t+h) = 1 + hi_h(t)

A = CA(t_1,t_2) because A(t,t+h) = A(t_1,t_2)

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

As we know that the accumulation A = CA(t_1,t_2)

Next: Accumulation Factor Ratio