Question

After 16 years in an account with a 5.9% annual interest rate compounded continuously, an investment is worth a total of $37,950.24. What is the value of the principal investment? Round the answer to the nearest penny. $14,765.24 $14,859.72 $23,185.00 $23,090.52

Answer 1

Answer: We can use the formula A = Pert to find the value of the principal investment P

Where A is the future value of the investment, r is the annual interest rate, t is the number of years, and e is the mathematical constant approximately equal to 2.718

In this case,

A = 37950.24, r = 0.059, t = 16

We can plug in the given values into the formula and solve for P:

37950.24 = P * e^(0.059 * 16)

To find the value of P we will divide both sides by e^(0.059 * 16)

P = 37950.24 / e^(0.059 * 16)

using the calculator to find the value of e^(0.059 * 16) gives 1.966862298

P = 37950.24 / 1.966862298

The value of P is $19,169.99.

Rounded to the nearest penny $19170

Therefore, the answer is $19,170.00

Explanation:

Answer 2

A=Pe^rt
A is the account value
P is the principal
r is the interest rate as a decimal
t is time
e is a standard/set value 2.7182818

Plug in what we know and then we are solving for the P value.
37950.24=P(2.718)^(.059 x 16)
=14,765.24