In n years at effective interest rate i, what is the present worth formula, P?

In n years at effective interest rate i, what is the present worth formula, P?

• A. P=F/(1+i)^n
• B. P=F(1+i)^n
• C. P=F×i/n
• D. P=F(1+i)²

Answer: (A)

The present worth formula describes the relationship between future value and present value in the context of financial calculations involving interest. In this case, the formula aligns with the concept of discounting a future sum of money back to its present value, factoring in the time value of money. When you have a future value F that you expect to receive after n years at an effective interest rate i, you want to determine how much that future value is worth in today's dollars—this is the present worth P. The formula employed in this case is P = F / (1 + i)^n. Here’s why this formula is appropriate: 1. **Time Value of Money**: The underlying principle of the formula is that money today is worth more than the same amount in the future due to its potential earning capacity. The discounting process effectively adjusts for this. 2. **Exponential Decay**: The denominator (1 + i)^n represents the compound interest accumulation over n years. By dividing the future amount F by this term, you’re determining what amount today would grow to F in the future at the given interest rate over n years. 3. **Compounding Effect**: The formula assumes continuous compounding of interest over the n-year period,

The present worth formula describes the relationship between future value and present value in the context of financial calculations involving interest. In this case, the formula aligns with the concept of discounting a future sum of money back to its present value, factoring in the time value of money.

When you have a future value F that you expect to receive after n years at an effective interest rate i, you want to determine how much that future value is worth in today's dollars—this is the present worth P. The formula employed in this case is P = F / (1 + i)^n.

Here’s why this formula is appropriate:

1. Time Value of Money: The underlying principle of the formula is that money today is worth more than the same amount in the future due to its potential earning capacity. The discounting process effectively adjusts for this.

2. Exponential Decay: The denominator (1 + i)^n represents the compound interest accumulation over n years. By dividing the future amount F by this term, you’re determining what amount today would grow to F in the future at the given interest rate over n years.

3. Compounding Effect: The formula assumes continuous compounding of interest over the n-year period,