## Accumulation Factors, Future Value – Explained with Examples

**[Watch video for detailed explanation of concept with examples]**

Accumulation
factor is the accumulation at time t_{2} of an investment of 1 at time
t_{1}. It is denoted as A(t_{1}, t_{2}) for time t_{1
}< t_{2}. So, the accumulation at time t_{2} of an
investment P at time t_{1} is PA(t_{1}, t_{2}). If t_{1}
= 0, then it is common to denote A(n) for A(0, n).

For simple interest case, the accumulation factor can easily be defined as A(n) = (1+ni)

For
compound interest case, the accumulation factor is A(n) = (1 + i)n. It is also called
as compound value factor (CVF_{i,n}) or compound interest factor or
compound factor of a lump sum 1.

#### Numerical Problem

Q 1. An investor deposit $1000 in a bank account that accumulates to $1500 in 3 years. i) Calculate the accumulation factor A(0,3). ii) Calculate simple interest rate and compound interest rate pa for this investment.

**[Watch video for solution of this numerical problem]**