Denise G. answered • 10/30/19

Algebra, College Algebra, Prealgebra, Precalculus, GED, ASVAB Tutor

a. The formula for compound interest: A=P(1+r/n)^{nt}

Plugging in values

6000=1000(1+.03/3)^{3t }Now this can be solved. Divide both sides of the equation by 1000

6000/1000=1000(1+.03/3)^{3t }/1000 Simplify

6=(1.01)^{3t} Take the log of both sides of the equation

log(6)=3t(log(1.01)) Divide both sides by 3(log(1.01))

log(6)/[3(log(1.01))]=3t(log(1.01))/[3(log(1.01))] Simplify

**60.0 = t**

b. The formula for continuous compounding is A=Pe^{rt}

Plugging in values

6000=1000(e)^{0.03t }Now this can be solved. Divide both sides of the equation by 1000

6000/1000=1000(e)^{0.03t}/1000 Simplify

6=(e)^{0.03t} Take the ln of both sides

ln(6)=0.03t(ln(e)) Simplify

ln(6)=0.03t Divide both sides by 0.03

ln(6)/0/03=0.03t/0.03

**59.7=t**