To solve this problem, we need to use the formula for continuous compounding, which is:

A = P * e^(rt)

Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money)
r = the annual interest rate (in decimal)
t = time (the number of years)

We know that A = $165,000, r = 10% or 0.10, t = 5 years, and we are solving for P.

So, we rearrange the formula to solve for P:

P = A / e^(rt)

Substituting the given values:

P = $165,000 / e^(0.10*5)

P = $165,000 / e^0.5

Using the given value of e = 2.71, we calculate:

P = $165,000 / 2.71^0.5

After calculating the above expression, we get P = $122,383.81

So, the closest answer is b. $130,000.

Question

To solve this problem, we need to use the formula for continuous compounding, which is:

A = P * e^(rt)

Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money)
r = the annual interest rate (in decimal)
t = time (the number of years)

We know that A = $165,000, r = 10% or 0.10, t = 5 years, and we are solving for P.

So, we rearrange the formula to solve for P:

P = A / e^(rt)

Substituting the given values:

P = $165,000 / e^(0.10*5)

P = $165,000 / e^0.5

Using the given value of e = 2.71, we calculate:

P = $165,000 / 2.71^0.5

After calculating the above expression, we get P = $122,383.81

So, the closest answer is b. $130,000.

Knowee AI · Accepted Answer