State True or False: The relation between accumulated value ‘A’and present value ‘P’ is `A= P(1+i)^n`

Answer

To determine whether the statement "The relation between accumulated value ‘A’ and present value ‘P’ is A = P(1+i)^n" is true or false, we can analyze the formula step by step.

### Step-by-Step Solution:

1. **Understanding the Terms:**
- **Present Value (P)**: This is the current value of a sum of money that will be received or paid in the future, discounted back to the present using a specific interest rate.
- **Accumulated Value (A)**: This is the future value of the present amount after interest has been applied over a certain period.

2. **Identifying the Formula:**
- The formula given is A = P(1+i)^n, where:
- A = Accumulated Value (Future Value)
- P = Present Value
- i = Interest Rate (expressed as a decimal)
- n = Number of compounding periods (years)

3. **Understanding Compound Interest:**
- The formula for compound interest states that the future value (A) can be calculated from the present value (P) by applying the interest rate (i) over n periods.
- This formula is derived from the principle of compounding, where the interest earned in each period is added to the principal for the calculation of interest in the next period.

4. **Substituting Values:**
- If we assume i is the interest rate per period and n is the total number of periods, then the formula correctly represents the relationship between present value and accumulated value.

5. **Conclusion:**
- Since the formula A = P(1+i)^n accurately describes the relationship between the accumulated value and present value in the context of compound interest, we can conclude that the statement is true.

### Final Answer:
**True**