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=Pert
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