Question

Ella invested $2,700 in an account paying an interest rate of 5.4% compounded

Answer 1

Answer:

7  

Step-by-step explanation:

Answer 2

Answer:

The account will take 7 years to reach a value of $4,020

Step-by-step explanation:

Compound Interest

When it occurs interest in the next period is then earned on the principal sum plus previously accumulated interest.

The formula is:

${\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}$

Where:

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Ella invested P=$2,700 in an account with an interest rate of r=5.4% (0.054) compounded monthly. Since there are 12 months in a year, n=12.

It will be calculated when will the account have a value of A=$4,020. Substituting all the values in the formula:

${\displaystyle 4,020=2,700\left(1+{\frac {0.054}{12}}\right)^{12t}}$

Calculating:

${\displaystyle 4,020=2,700\left(1.0045)^{12t}}$

Dividing by 2,700:

${\displaystyle \frac{4,020}{2,700}=\left(1.0045)^{12t}}$

To solve this equation for t, we need to apply logarithms:

${\displaystyle \log\frac{4,020}{2,700}=\log\left(1.0045)^{12t}}$

Applying the logarithm power rule:

$\displaystyle \log\frac{4,020}{2,700}=12t\log 1.0045$

Dividing by 12log 1.0045:

$\displaystyle t=\frac{\log\frac{4,020}{2,700}}{12\log 1.0045}$

Calculating:

t= 7.39 years

Rounding to the nearest year, the account will take 7 years to reach a value of $4,020