Can someone help me with this Algebra 2 question?

Question

A principal of $1500 is invested at 3.5 percent interest, compounded annually. How many years will it take to accumulate $2000 or more in the account?

Answer 1

The equation for compound interest is:

 

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

 

Where:

• A(t) = the value of the investment at time t = $2000
• P = the initial principle = $1500
• r = the annual interest rate expressed as a decimal = 3.5% = 0.035
• n = the number of compounding per year = annual = 1
• t = years

 

$2000 = $1500(1 + 0.035/1)^1*t

4/3 = (1.035)^t

log(4/3) = log(1.035^t)

 

Use the identity log(a^b) = b*log(a)

 

log(4/3) = t*log(1.035)

log(4/3)/log(1.035) = t

 

8.36 years ≅ t