Final answer:
To determine the amount you would be willing to lend to your brother, you can calculate the present value of the promised payment using the formula PV = FV / (1 + r)^n. Plugging in the values, the present value is $6,853.87.
Step-by-step explanation:
To calculate the amount you would be willing to lend to your brother, you need to determine the present value of the promised payment of $8,600 at the end of three years. Given that you normally invest to earn 7.70 percent per year, the present value can be calculated using the formula:
PV = FV / (1 + r)^n
Where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods. Plugging in the values, we get:
PV = $8,600 / (1 + 0.077)^3 = $8,600 / 1.254407 = $6853.87
Therefore, you would be willing to lend your brother $6,853.87 if you view this purely as a financial transaction.
To maintain the earning power equivalent to a 7.70 percent annual investment, you would be willing to lend your brother approximately $6,922.76 today for a promise to be repaid $8,600 in three years.
The question involves evaluating a financial decision using the concept of present value to establish how much a future sum of money is worth today given a specific interest rate. To find out how much you would be willing to lend your brother considering a 7.70 percent annual interest rate, you would use the present value formula: PV = FV / (1 + r)^n, where PV is the present value, FV is the future value ($8,600), r is the annual interest rate (7.70 percent or 0.077), and n is the number of years (3).
Plugging in the values, the calculation would be:
PV = $8,600 / (1 + 0.077)^3
PV = $8,600 / (1.077)^3
PV = $8,600 / 1.242287
PV ≈ $6,922.76
Thus, you would be willing to lend approximately $6,922.76 to your brother if you want to maintain the same earning power as your normal investments at 7.70 percent.