Final answer:
The present value is the valuation in today's dollars of a future sum of money, discounted by a specific interest rate over a set number of years. To find the present values for each scenario, you apply the standard present value formula with the given interest rates and periods, then sum them up for the final answer.
Step-by-step explanation:
To calculate the present value of a future sum of money, we use the present value formula, which discounts the future amount by the given interest rate for the number of years until the payment will be received. The formula for present value (PV) is:
PV = FV / (1 + r)^n
where FV is the future value, r is the interest rate (expressed as a decimal), and n is the number of periods (years) until the payment will be received.
-
- The present value of $8,000 in 10 years at 6 percent is calculated as $8,000 / (1 + 0.06)^10.
-
- The present value of $16,000 in 5 years at 12 percent is $16,000 / (1 + 0.12)^5.
-
- The present value of $25,000 in 15 years at 8 percent is $25,000 / (1 + 0.08)^15.
-
- The present value of $1,000 in 40 years at 20 percent is $1,000 / (1 + 0.20)^40.
After calculating each of these, you would add up all the present values to get the final answer. The present value calculations are critical for understanding how much an amount of money to be received in the future is worth in today's terms, especially when considering investments, loans, and financial planning.