Answer:
The present value is $537.78
Explanation:
Given
[tex]Future\ Value\ (FV) = \$20,000\\Time (T) = 50\ Years\\Discount\ Rate\ (R)= 7.5\%[/tex]
Required
The Present Value(I)
To calculate the present value, we simply apply the formula for future value;
[tex]FV = I *(1 + R)^T[/tex]
Substitute 20,000 for FV; 50 for T and 7.5% for R;
This gives
[tex]20,000 = I *(1 + 7.5\%)^{50}[/tex]
Convert percent to decimal
[tex]20,000 = I *(1 + 0.075)^{50}[/tex]
[tex]20,000 = I *(1.075)^{50}[/tex]
[tex]20,000 = I *37.19[/tex]
Divide both sides by 37.19
[tex]\frac{20,000}{37.19} = \frac{I *37.19}{37.19}[/tex]
[tex]\frac{20,000}{37.19} = I[/tex]
[tex]537.778 = I[/tex]
[tex]I = 547.78\ (Approximated)[/tex]
Hence, the present value is $537.78
