Respuesta :
Answer:
Dot number 2. Makayla invests her money 2 years longer.
Step-by-step explanation:
Calvin 400$ with 5% interest compounded monthly will get you to 666.0294029241$ after 13 months or 1 year and 1 month
Makayla 300$ with 6% interest quarterly
1st year 378.743088$(4 quarters)
2nd year 478.1544223592$(+4 quarters)
3rd year 603.6589415506$(+4 quarters)
3rd year and 1 quarter 639.8784780436$
Answer:
So the second option is the answer: Makayla invests her money 2 years longer.
Step-by-step explanation:
Formula for compound interest: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Calvin:
[tex]A=658.80[/tex]
[tex]P=400[/tex]
[tex]r=0.05[/tex]
[tex]n=12[/tex]
[tex]t=?[/tex]
Makayla:
[tex]A=613.04[/tex]
[tex]P=300[/tex]
[tex]r=0.06[/tex]
[tex]n=4[/tex]
[tex]t=?[/tex]
Lets solve for [tex]t[/tex].
1) Divide both sides of the equation by [tex]P[/tex].
[tex]\frac{A}{P} =(1+\frac{r}{n})^{nt}[/tex]
2) Take the natural log of both sides.
[tex]ln(\frac{A}{P}) =ln((1+\frac{r}{n})^{nt})[/tex]
3) Rewrite the right side of the equation using properties of exponents.
[tex]ln(\frac{A}{P}) =nt*ln(1+\frac{r}{n})[/tex]
4) Divide each side of the equation by [tex]n*ln(1+\frac{r}{n})[/tex]
[tex]\frac{nt*ln(1+\frac{r}n)}{n*ln(1+\frac{r}n)}=\frac{ln(\frac{A}{P})}{n*ln(1+\frac{r}n)}[/tex]
5) Cancel the common factor [tex]n[/tex] on the left side of the equation.
[tex]\frac{t*ln(1+\frac{r}n)}{ln(1+\frac{r}n)}=\frac{ln(\frac{A}{P})}{n*ln(1+\frac{r}n)}[/tex]
6) Cancel the common factor of [tex]ln(1+\frac{r}{n})[/tex].
[tex]t=\frac{ln(\frac{A}{P)}}{n*ln(1+\frac{r}{n})}[/tex]
Now we have an equation for [tex]t[/tex] that we can use to answer your question.
For Calvin:
[tex]t=\frac{ln(\frac{658.80}{400)}}{12*ln(1+\frac{0.05}{12})}[/tex]
[tex]t=10[/tex]
For Makayla:
[tex]t=\frac{ln(\frac{613.04}{300)}}{3*ln(1+\frac{0.06}{3})}[/tex]
[tex]t=12[/tex]
So the second option is the answer: Makayla invests her money 2 years longer.
Note: This question took me 2 minutes to answer but typing it took 30. lol
