Your trust fund will pay you $100.000 in six years when you turn 25. A shady institute has encourage you to sign over in exchange of cash today. Would you prefer a 8% or 10% discount rate to determine value of lump sum payment ?
A. Use 8% the lump sum is $62, 741 is greater than 10% of $55,839.
B. Use 10% the lump sum is $62, 741 is greater than 10% of $55, 839.
C. Use 8% , the lump sum is $63,017 is greater than 10% of $56,447.
D. Use 10% the lump sum is $63,017 is greater than 10% of $56,447
1.10^6 = 1.77
1.08^6 = 1.59
100,000/1.77 = 56,447 using 10%
100,000/1.59 = 63,017 using 8%
so C
Thanks
To determine the present value of the trust fund payment, you can use the concept of discounting. Discounting is a method to calculate the current value of a future payment by considering the time value of money.
In this case, you need to decide between using an 8% or 10% discount rate to calculate the lump sum payment. The higher the discount rate, the lower the present value of the future payment.
Let's calculate the present value using both discount rates and compare the results:
1. Using an 8% discount rate:
To calculate the present value at an 8% discount rate, you can use the formula:
Present Value = Future Value / (1 + Discount Rate)^n
Where:
Future Value = $100,000 (the trust fund payment)
Discount Rate = 8% (0.08)
n = 6 years (the time until the payment is received)
Present Value = $100,000 / (1 + 0.08)^6
Present Value = $55,839.02
2. Using a 10% discount rate:
To calculate the present value at a 10% discount rate, you can use the same formula:
Present Value = Future Value / (1 + Discount Rate)^n
Where:
Future Value = $100,000 (the trust fund payment)
Discount Rate = 10% (0.10)
n = 6 years (the time until the payment is received)
Present Value = $100,000 / (1 + 0.10)^6
Present Value = $62,741.14
Now, let's compare the calculated present values with the given options:
A. Use 8%, the lump sum is $62,741, which is greater than 10% of $55,839. [Incorrect statement]
B. Use 10%, the lump sum is $62,741, which is greater than 10% of $55,839. [Correct statement]
C. Use 8%, the lump sum is $63,017, which is greater than 10% of $56,447. [Incorrect statement]
D. Use 10%, the lump sum is $63,017, which is greater than 10% of $56,447. [Incorrect statement]
Therefore, the correct statement is B. Use 10%, the lump sum is $62,741, which is greater than 10% of $55,839.