# Solve for t 2500=1200(1+0.08/12)^(12*t)

2500=1200(1+0.0812)12⋅t
Rewrite the equation as 1200(1+0.0812)12⋅t=2500.
1200(1+0.0812)12⋅t=2500
Simplify.
Divide 0.08 by 12.
1200(1+0.006‾)12⋅t=2500
Add 1 and 0.006‾.
1200⋅1.006‾12⋅t=2500
1200⋅1.006‾12⋅t=2500
Divide each term by 1200 and simplify.
Divide each term in 1200⋅1.006‾12⋅t=2500 by 1200.
1200⋅1.006‾12⋅t1200=25001200
Cancel the common factor of 1200.
Cancel the common factor.
1200⋅1.006‾12⋅t1200=25001200
Divide 1.006‾12⋅t by 1.
1.006‾12⋅t=25001200
1.006‾12t=25001200
Cancel the common factor of 2500 and 1200.
Factor 100 out of 2500.
1.006‾12t=100(25)1200
Cancel the common factors.
Factor 100 out of 1200.
1.006‾12t=100⋅25100⋅12
Cancel the common factor.
1.006‾12t=100⋅25100⋅12
Rewrite the expression.
1.006‾12t=2512
1.006‾12t=2512
1.006‾12t=2512
1.006‾12t=2512
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln(1.006‾12t)=ln(2512)
Expand ln(1.006‾12t) by moving 12t outside the logarithm.
12tln(1.006‾)=ln(2512)
Divide each term by 12ln(1.006‾) and simplify.
Divide each term in 12tln(1.006‾)=ln(2512) by 12ln(1.006‾).
12tln(1.006‾)12ln(1.006‾)=ln(2512)12ln(1.006‾)
Simplify 12tln(1.006‾)12ln(1.006‾).
Cancel the common factor of 12.
Cancel the common factor.
12tln(1.006‾)12ln(1.006‾)=ln(2512)12ln(1.006‾)
Rewrite the expression.
tln(1.006‾)ln(1.006‾)=ln(2512)12ln(1.006‾)
tln(1.006‾)ln(1.006‾)=ln(2512)12ln(1.006‾)
Cancel the common factor of ln(1.006‾).
Cancel the common factor.
tln(1.006‾)ln(1.006‾)=ln(2512)12ln(1.006‾)
Divide t by 1.
t=ln(2512)12ln(1.006‾)
t=ln(2512)12ln(1.006‾)
t=ln(2512)12ln(1.006‾)
t=ln(2512)12ln(1.006‾)
The result can be shown in multiple forms.
Exact Form:
t=ln(2512)12ln(1.006‾)
Decimal Form:
t=9.20516287…
Solve for t 2500=1200(1+0.08/12)^(12*t)

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