Pearson corporation makes an investment today (January 1, 2010). They will receive $10,000 every December 31st for the next six years (2010-2015) If pearson wants to earn 12% on the investment, what is the most they should invest on January 1, 2010? A) $41,114 B) $46,048 C) $81,152 D) $90,890
To calculate the most Pearson should invest, we can use the concept of present value. Present value is the current value of a future amount of money, taking into account the time value of money.
The formula for present value is:
PV = FV / (1 + r)^n
Where:
PV = Present Value
FV = Future Value
r = Rate of return (interest rate)
n = Number of periods
In this case, Pearson wants to earn a 12% return, so r = 0.12, and they will receive $10,000 each year for six years, so n = 6. We need to find the present value (PV).
Let's calculate the present value for each $10,000 that Pearson will receive and then sum them up:
PV1 = $10,000 / (1 + 0.12)^1
PV2 = $10,000 / (1 + 0.12)^2
PV3 = $10,000 / (1 + 0.12)^3
PV4 = $10,000 / (1 + 0.12)^4
PV5 = $10,000 / (1 + 0.12)^5
PV6 = $10,000 / (1 + 0.12)^6
Now let's calculate each present value:
PV1 = $10,000 / (1.12)^1 = $8,928.57
PV2 = $10,000 / (1.12)^2 = $7,991.07
PV3 = $10,000 / (1.12)^3 = $7,145.65
PV4 = $10,000 / (1.12)^4 = $6,384.28
PV5 = $10,000 / (1.12)^5 = $5,699.75
PV6 = $10,000 / (1.12)^6 = $5,085.79
Now, let's sum up all the present values:
Total PV = PV1 + PV2 + PV3 + PV4 + PV5 + PV6
Total PV = $8,928.57 + $7,991.07 + $7,145.65 + $6,384.28 + $5,699.75 + $5,085.79
Total PV = $41,234.11
Therefore, the most Pearson should invest on January 1, 2010, is approximately $41,234.11.
Among the given answer choices, the closest option is A) $41,114.