Question

Cynthia invested $12,000 in a savings account. If the interest rate is 6%, how much will be in the account in 10 years by compounding continuously? Round to the nearest cent.

Answer 1

Answer:

In 10 years she'll have approximately $21865.4 in her account.

Step-by-step explanation:

When an amount is compounded continuously its value over time is given by the following expression:

$v(t) = v(0)*e^{rt}$

Applying data from the problem gives us:

$v(10) = 12000*e^{(0.06*10)}\\v(10) = 12000*e^{0.6}\\v(10) = 21865.4$

In 10 years she'll have approximately $21865.4 in her account.

Answer 2

Answer: A= $21,768.22

Step-by-step explanation:

Identify the values of each variable in the formulas.

A=?

P= $12,000

r= 0.06

t= 10

For quarterly composing, n=4. There are 4 quarters in a year.

A= P(1+r/n)^nt

Substitute the values in the formula

A= 12,000( 1+ 0.06/4)^4*10

Commute the amount

A= $21,768.22