To solve this problem, we will 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 = principal amount (the initial amount of money)
r = annual interest rate (in decimal)
t = time the money is invested for, in years

Given in the problem:
P = $9,000
r = 4.4% or 0.044 (in decimal)
t = 13 years

Substituting these values into the formula, we get:

A = 9000 * e^(0.044*13)

Now, calculate the exponent part first:

0.044 * 13 = 0.572

So, the equation becomes:

A = 9000 * e^0.572

Now, use the value of e (approximately equal to 2.71828) and raise it to the power of 0.572:

e^0.572 = 1.77245

Now, multiply this result by the principal amount:

A = 9000 * 1.77245

A = $15,952.05

So, Mrs. Sandy will have approximately $15,952.05 in her bank account in 13 years.

Question

To solve this problem, we will 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 = principal amount (the initial amount of money)
r = annual interest rate (in decimal)
t = time the money is invested for, in years

Given in the problem:
P = $9,000
r = 4.4% or 0.044 (in decimal)
t = 13 years

Substituting these values into the formula, we get:

A = 9000 * e^(0.044*13)

Now, calculate the exponent part first:

0.044 * 13 = 0.572

So, the equation becomes:

A = 9000 * e^0.572

Now, use the value of e (approximately equal to 2.71828) and raise it to the power of 0.572:

e^0.572 = 1.77245

Now, multiply this result by the principal amount:

A = 9000 * 1.77245

A = $15,952.05

So, Mrs. Sandy will have approximately $15,952.05 in her bank account in 13 years.

Knowee AI · Accepted Answer