Question

The purchasing power P (in dollars) of an annual amount of A dollars after † years of 5% inflation decays according to the following formula. P=

E-0.05t How long will it be before a pension of $90,000 per year has a purchasing power of $20,000?

Answer 1

It will be approximately 17.36 years before a pension of $90,000 per year has a purchasing power of $20,000.

Step-by-step explanation:

To find out how long it will be before a pension of $90,000 per year has a purchasing power of $20,000, we can use the formula P = E^(−0.05t). In this case, P represents the purchasing power, which is $20,000, and E represents the annual amount of the pension, which is $90,000. Let's substitute these values into the formula and solve for t:

20,000 = 90,000 * e^(−0.05t)

Divide both sides of the equation by 90,000:

0.22 = e^(−0.05t)

Take the natural logarithm of both sides of the equation:

ln(0.22) = −0.05t

Divide both sides of the equation by −0.05:

t = ln(0.22) / −0.05

Using a calculator, we find that t is approximately 17.36 years. Therefore, it will be approximately 17.36 years before the purchasing power of a $90,000 per year pension reaches $20,000.