Question

If you could invest your money at 8% compounded annually, which option should you pick? a. (1), because it has a higher PV. b. You are indifferent between the two choices. c. (2), because it has a higher PV. d. You do not have enough information to make that decision.

Answer 1

If you could invest your money at 8% compounded annually,You should pick Option c. (2), because it has a higher PV.

Step-by-step explanation:

Choosing the investment with a higher present value (PV) is crucial for maximizing returns over time. In this scenario, the option with the higher PV is (2), making it the more favorable choice. The present value is an essential metric in financial decision-making, representing the current worth of future cash flows discounted at a specific rate.

Firstly, let's understand the concept of present value. It is calculated using the formula:

`\[PV = (FV)/((1 + r)^n)\]`

where FV is the future value, r is the interest rate per compounding period, and n is the number of compounding periods. Since we are comparing options compounded annually at 8%, the formula simplifies to:

`\[PV = (FV)/((1 + 0.08)^n)\]`

Now, comparing the present values of options (1) and (2), if all other factors are equal, and assuming the same future value and compounding periods, the option with the higher present value is the better investment. It's important to note that this decision is based solely on the present value comparison, and other factors such as risk, liquidity, and investment goals should also be considered in real-world scenarios.

In conclusion, the answer is (c) because choosing the option with a higher present value aligns with sound financial principles, ensuring a more lucrative investment in the long run.