What is the present value of \$1,200 to be received in 18 years if the discount rate is 5\% per year, compounded annually?

• A. \$1,080.00
• B. \$900.00
• C. \$1,200.00
• D. \$537.13

Answer: (D)

Verified step by step guidance

1. Step 1: Understand the concept of present value (PV). Present value is the current worth of a future sum of money, discounted at a specific interest rate over a given period of time. The formula for calculating PV is: PV = FV / (1 + r)^n, where FV is the future value, r is the annual discount rate, and n is the number of years.
2. Step 2: Identify the values given in the problem. The future value (FV) is \$1,200, the discount rate (r) is 5% or 0.05, and the number of years (n) is 18.
3. Step 3: Substitute the given values into the formula. Using MathML, the formula becomes: $\mathrm{PV}=\frac{\mathrm{FV}}{{\left(1+r\right)}^{}n}$. Replace FV with 1200, r with 0.05, and n with 18.
4. Step 4: Simplify the denominator. Calculate (1 + r)^n, which is (1 + 0.05)^18. This involves raising 1.05 to the power of 18.
5. Step 5: Divide the future value (FV) by the calculated denominator. This will give you the present value (PV). Ensure you understand the importance of discounting future cash flows to their present value in financial decision-making.