Final answer:
To accumulate $20,000 in an account with 6% interest in 5 years, the amount you must deposit now is $14,945.20. This is calculated using the compound interest formula. Starting early and utilizing compound interest can significantly increase savings over time.
Step-by-step explanation:
The question asks for the present value of a future sum of money when interest is compounded, which is a common problem in financial mathematics. To accumulate $20,000 in 5 years with an account paying 6% interest, you must find the present value using the formula:
PV = FV / (1 + r)n
Where PV is the present value, FV is the future value ($20,000), r is the annual interest rate (6% or 0.06), and n is the number of years (5).
Solving this, we get:
PV = $20,000 / (1 + 0.06)5 = $20,000 / (1.338225577)
= $14,945.20
So, the correct answer is b. $14,945.20.
Starting to save money early and taking advantage of the power of compound interest can yield impressive results over time. For example, $3,000 invested at a 7% annual rate of return for 40 years grows to approximately $44,923.