An IRA has ​$11,000 in​ it, and the owner decides not add any more money to the account other than interest earned at 4​% compounded daily. How much will be in the account 40 years from now?

Answer 1

Formula Used: FV= PV × (1+(r/c))^c*y

Note: Where the Future Value of an investment (FV) equals the Present Value (PV) multiplied by one plus the annual interest rate (r) divided by the annual compounding periods (c) raised to the power of annual compounding periods (c) multiplied by number of accruement years (y).

For our problem, the Individual Retirement Account (IRA) has a PV of $11,000 which has an annual interest rate (r) of 4% or 0.04. Notice it compounds daily! This affects both our compounding time as well as the interest rate. Meaning, our annual compounding period (c) is 365 times per year multiplied by 40 years (365 x 40 = 14,600) and our interest rate is going to be divided up among all days of the year (0.04 ÷ 365 = 0.00010959).

Formula Input: FV = 11,000 x (1+(0.04/365))^365*40

Formula Simplified: FV = 11,000 x (1.00010959)^14,600

Formula Solved: FV = 11,000 x 4.95267 = $54,479.34

Explanation: The solution derived shows that the IRA with $11,000 invested today will be worth $54,479.34 based on 40 years of accruing a 4% annual interest and daily compounding.