What is the correct future value formula for annual compounding?

What is the correct future value formula for annual compounding?

• A. FV = PV × (1 + r)^(n-1)
• B. FV = PV × (1 + r)^(n+1)
• C. FV = PV × (1 + r)^n
• D. FV = PV × (1 + r)^n - 1

Answer: (C)

Annual compounding grows the balance by a factor of 1 + r each year. After n years, those growth factors stack, so the amount you end up with is PV multiplied by (1 + r) n times: FV = PV × (1 + r)^n. For example, with PV = 1000, r = 0.05, and n = 3, you get FV ≈ 1000 × (1.05)^3 ≈ 1157.63. Using an exponent of n−1 would miss one year of growth, giving too small a value. An exponent of n+1 would add an extra year of growth, giving too large a value. Subtracting 1 after the growth (PV × (1 + r)^n − 1) incorrectly alters the total, since future value of a lump sum doesn’t require subtracting 1.

Annual compounding grows the balance by a factor of 1 + r each year. After n years, those growth factors stack, so the amount you end up with is PV multiplied by (1 + r) n times: FV = PV × (1 + r)^n.

For example, with PV = 1000, r = 0.05, and n = 3, you get FV ≈ 1000 × (1.05)^3 ≈ 1157.63.

Using an exponent of n−1 would miss one year of growth, giving too small a value. An exponent of n+1 would add an extra year of growth, giving too large a value. Subtracting 1 after the growth (PV × (1 + r)^n − 1) incorrectly alters the total, since future value of a lump sum doesn’t require subtracting 1.