Ella invested $2,700 in an account paying an interest rate of 5.4% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to
the nearest year, for the value of the account to reach $4,020?

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:

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:

Calculating:

Dividing by 2,700:

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

Applying the logarithm power rule:

Dividing by 12log 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