To calculate the present value of $3 billion discounted over 10 years at a 10% discount rate, you can use the present value formula:
[
text{Present Value} = frac{text{Future Value}}{(1 + r)^n}
]
where:
– **Future Value (FV)** = $3 billion
– **Discount Rate (r)** = 10% or 0.10
– **Number of Periods (n)** = 10 years
Substituting these values into the formula gives:
[
text{Present Value} = frac{3,000,000,000}{(1 + 0.10)^{10}} approx frac{3,000,000,000}{2.5937} approx 1,156,492,000
]
Therefore, the present value of $3 billion discounted over 10 years at a 10% discount rate is approximately $1.16 billion.
This calculation assumes that the $3 billion is received all at once after 10 years and that the discount rate remains constant over that period. The choice of discount rate can significantly affect the present value, as higher rates reduce the present value and lower rates increase it[1][4].
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