How do you solve 120=100(1+(.032/12))^(12t)?

2 Answers
Nov 14, 2015

Use logarithms.

Explanation:

Divide both sides by 100: 1.2=(1+(.032/12))^(12t)
Simplify the inside: 1.2=(1.002bar6)^(12t)
Convert into a logarithm: log_"1.2"1.002bar6=12t
Change of base formula: (log1.002bar6)/log1.2=12t
Divide both sides by 12: color(blue)((log1.002bar6)/(12log1.2)=t

Nov 14, 2015

t= ln(6/5)/(12ln(1+.032/12))

Explanation:

We will be using the property of logarithms that
ln(x^n) = nln(x)
(this is very useful for solving for variables in exponents)

120 = 100(1+.032/12)^(12t)

=>120/100= 6/5 = (1+.032/12)^(12t)

=>ln(6/5) = ln((1+.032/12)^(12t))

=> ln(6/5) = 12tln(1+.032/12) (by the property stated above)

Now, solving for t gives

t = ln(6/5)/(12ln(1+.032/12))