Answer:
<em>The account will take 7 years to reach a value of $4,020</em>
Step-by-step explanation:
<u>Compound Interest </u>
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