In n years at effective interest rate i, what is the formula for calculating an investment's present worth, P?

The formula for calculating the present worth ( P ) of an investment, given its future value ( F ), the effective interest rate ( i ), and the number of years ( n ), is derived from the concept of time value of money. The present worth is essentially the value today of a future sum of money, discounted back to the present using the interest rate.

The correct formula, ( P = F / (1 + i)^n ), reflects the process of discounting. It indicates that to find the present worth ( P ), the future value ( F ) must be divided by the factor ( (1 + i)^n ). This factor accounts for the accumulated interest over ( n ) years at the effective interest rate ( i ). By using this formula, you determine how much the future amount is worth in today’s terms.

In summary, the formula emphasizes the principle of discounting future cash flows to their present value, showcasing the inverse relationship between present value and future value in relation to interest accrual over time.