# 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

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

Where,

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

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

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

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