Find how long it takes $1500 to double if it is invested at 7% interest compound semiannually. Use the formula A=P (1+r/n)^nt to solve the compound interest problem.
It will take approximately ? Years .
Round to the nearest tenth as needed.
[tex]A=P(1+ \frac{r}{n})^ \frac{t}{n} [/tex] A=future amount P=present amount r=rate in decimal n=number of times per year compounded t=time in years
how many years to double basically A=2P at t=? so we can simplify and ignore the pricipal given and do [tex]2=(1+ \frac{r}{n})^ \frac{t}{n} [/tex] r=7%=0.07 n=2 (semiannualy means 2 times per year) t=t
[tex]2=(1+ \frac{0.07}{2})^ \frac{t}{2} [/tex] [tex]2=(1+ 0.035)^ \frac{t}{2} [/tex] [tex]2=(1.035)^ \frac{t}{2} [/tex] take the ln of both sides [tex]ln2=(\frac{t}{2})ln1.035 [/tex] divide both sides by ln1.035 [tex] \frac{ln2}{ln1.035} = \frac{t}{2} [/tex] times 2 both sides [tex] \frac{2ln2}{ln1.035} =t [/tex] use calculator 40.2976=t nearest tenth 40.3 about 40.3 years
