Answer:
<em>a. $42,572 at 2%, </em>
<em>b. $35,559 at 5% </em>
<em>c. $29,702 at 8% </em>
Step-by-step explanation:
The formula used for FV calculation for Continuous Compounding is as under:
![FV = PV e^{i * t}](https://tex.z-dn.net/?f=FV%20%3D%20PV%20e%5E%7Bi%20%2A%20t%7D)
Where,
FV = Future Value = $8000 each year (At the end of 6 years = $8000 x 6 = $48,000)
PV = Present Value
e = Mathematical Constant = 2.713
i = Interest Rate
t= time in years
a) For 2%:
![FV = PV e^{i * t}\\48000 = PV e^{0.02 * 6}\\48000 = 1.1275 (PV)\\PV = 42,572](https://tex.z-dn.net/?f=FV%20%3D%20PV%20e%5E%7Bi%20%2A%20t%7D%5C%5C48000%20%3D%20PV%20e%5E%7B0.02%20%2A%206%7D%5C%5C48000%20%3D%201.1275%20%28PV%29%5C%5CPV%20%3D%2042%2C572)
b) For 5%:;
![FV = PV e^{i * t}\\48000 = PV e^{0.05 * 6}\\48000 = 1.35 (PV)\\PV = 35,559\\](https://tex.z-dn.net/?f=FV%20%3D%20PV%20e%5E%7Bi%20%2A%20t%7D%5C%5C48000%20%3D%20PV%20e%5E%7B0.05%20%2A%206%7D%5C%5C48000%20%3D%201.35%20%28PV%29%5C%5CPV%20%3D%2035%2C559%5C%5C)
c) For 8%:
![FV = PV e^{i * t}\\48000 = PV e^{0.08 * 6}\\48000 = 1.616 (PV)\\PV = 29,702](https://tex.z-dn.net/?f=FV%20%3D%20PV%20e%5E%7Bi%20%2A%20t%7D%5C%5C48000%20%3D%20PV%20e%5E%7B0.08%20%2A%206%7D%5C%5C48000%20%3D%201.616%20%28PV%29%5C%5CPV%20%3D%2029%2C702)
Note: <em>Investing $42,572 at 2%, $35,559 at 5% and $29,702 at 8% today will get $48,000 at the end of 6 years. </em>