mordica company will receive $100,000 in 7 years. If the appropriate interest rate is 10%, the present value of the $100,000 receipt is (A) $51,000 (B) $51,316 (c) $151,000 (D) $194,872
To calculate the present value of the $100,000 receipt, we need to discount it back to the present using the appropriate interest rate. The formula for calculating the present value is:
Present value = Future value / (1 + i)^n
Where:
- Future value is the value of the receipt in the future ($100,000 in this case)
- i is the interest rate (10% or 0.10 as a decimal)
- n is the number of years (7 years in this case)
Let's substitute the given values into the formula and calculate the present value:
Present value = $100,000 / (1 + 0.10)^7
Now, let's solve this equation:
Present value = $100,000 / (1.10)^7
= $100,000 / 1.948717
≈ $51,316
Therefore, the present value of the $100,000 receipt is approximately $51,316.
The correct answer is (B) $51,316.
To find the present value of the $100,000 receipt, we can use the formula for present value of a future cash flow:
Present Value = Future Value / (1 + Interest Rate)^n
Where:
Future Value = $100,000
Interest Rate = 10% or 0.10
n = number of years = 7
Plugging in the values:
Present Value = $100,000 / (1 + 0.10)^7
Present Value = $100,000 / (1.10)^7
Present Value = $100,000 / 1.948717
Calculating the division:
Present Value ≈ $100,000 / 1.948717
Present Value ≈ $51,316
Therefore, the present value of the $100,000 receipt is approximately $51,316.
Answer: (B) $51,316