Garland inc. offers a new employee a single-sum signing bonus at the date of employment, june 1, 2021. alternatively, the employee can receive $39,000 at the date of employment plus $10,000 each june 1 for five years, beginning in 2025. assuming the employee's time value of money is 9% annually, what single amount at the employment date would make the options equally desirable?

$69,030

The employee can decide to receive a single amount of $69,030 at the employment date.

Explanation:

The time value of money is the idea that money is worth more now, than the same amount a year or five years from now. You can buy more with $10,000 today than you will be able to in 2021 or 2025.

The formula for calculating the present value of money is  

or

Where PV is the present value

FV is the future value ($10,000)

r is the time value of money (9% or 0.09) and

n is the number of periods   (2025 to 2029).

In this question,

2021 is period 0. In 2021, the employee receives 39,000. This is the present value = 39000

2022 is period 1

2023 is period 2

2024 is period 3

2025 is period 4. In 2025, the employee will receive 10,000 so the present value, PV =

PV=10000 * 0.708 = 7080

2026 is period 5. In 2026, the employee will receive 10,000 so the present value, PV =

PV=10000 * 0.650 = 6500

2027 is period 6. In 2027, the employee will receive 10,000 so the present value, PV =

PV=10000 * 0.596 = 5960

2028 is period 7. In 2028, the employee will receive 10,000 so the present value, PV =

PV=10000 * 0.547 = 5470

2029 is period 8. In 2029, the employee will receive 10,000 so the present value, PV =

PV=10000 * 0.502 = 5020

In total, the present value = (39000 + 7080 + 6500  + 5960 + 5470 + 5020)

=69,030

The employee can decide to receive a single amount of $69030 at the employment date.

(You can also look up the values in a discount table and multiply them by the present value. Note that the first payment of $10,000 is in period 4, not 5. This is because 2021 is period 0)

b or d if i'm correct boi.