Suppose you were offered $2,000 to be delivered in 1 year. Further suppose you had the alternative of putting money into a safe certificate of deposit paying annual interest at 10 percent. Would you pay $1,900 in exchange for $2,000 after 1 year? What is the maximum amount you would pay for the offer of $2,000? Suppose the offer was $2,000, but delivery was to be in 2 years instead of 1 year. What is the maximum amount you would be willing to pay?
To determine whether it is worth paying $1,900 in exchange for $2,000 after 1 year, we can calculate the future value of investing $1,900 in a certificate of deposit (CD) with a 10% annual interest rate.
To calculate the future value of an investment with compound interest, we can use the formula:
Future Value = Principal * (1 + Interest Rate)^Time
In this case, the Principal is $1,900, the Interest Rate is 10% (or 0.10), and the Time is 1 year.
Future Value = $1,900 * (1 + 0.10)^1
Future Value = $1,900 * 1.10
Future Value = $2,090
Based on this calculation, if you invested $1,900 in a CD with a 10% annual interest rate for 1 year, it would grow to $2,090.
Comparing this to the offer of $2,000, it seems more advantageous to invest the money in the CD because it would yield a higher return ($2,090 > $2,000). Therefore, it would not be worth paying $1,900 for the offer of $2,000 after 1 year.
Now, let's calculate the maximum amount you would be willing to pay for the offer of $2,000 if the delivery was to be in 1 year:
Max Amount = Future Value / (1 + Interest Rate)^Time
Using the formula, we can substitute the Future Value ($2,000), Time (1 year), and Interest Rate (10%) into the equation:
Max Amount = $2,000 / (1 + 0.10)^1
Max Amount = $2,000 / 1.10
Max Amount ≈ $1,818.18
Therefore, the maximum amount you should be willing to pay for the offer of $2,000 to be delivered in 1 year is approximately $1,818.18.
Now, let's consider the scenario where the delivery is in 2 years instead of 1 year. To determine the maximum amount you would be willing to pay in this case, we need to calculate the future value of investing $1,900 in a CD with a 10% annual interest rate over 2 years:
Future Value = $1,900 * (1 + 0.10)^2
Future Value = $1,900 * 1.21
Future Value = $2,299
Using the formula, we find that the investment would grow to $2,299 over 2 years.
To calculate the maximum amount you would be willing to pay for the offer of $2,000 delivered in 2 years, you can use the same formula as before:
Max Amount = Future Value / (1 + Interest Rate)^Time
Max Amount = $2,000 / (1 + 0.10)^2
Max Amount = $2,000 / 1.21
Max Amount ≈ $1,652.89
Therefore, the maximum amount you should be willing to pay for the offer of $2,000 to be delivered in 2 years is approximately $1,652.89.