It takes 10.155 years until you have $3,000 ⇒ 3rd
Step-by-step explanation:
The formula for compound interest, including principal sum is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where
∵ You decide to put $2,000 in a savings account
∴ P = 2000
∵ You want to save for $3,000
∴ A = 3000
∵ The account has an interest rate of 4% per year and is
compounded monthly
∴ r = 4% = 4 ÷ 100 = 0.04
∴ n = 12 ⇒ compounded monthly
- Substitute all of these values in the formula above to find t
∵ [tex]3000=2000(1+\frac{0.04}{12})^{12t}[/tex]
- Divide both sides by 2000
∴ [tex]1.5=(1+\frac{1}{300})^{12t}[/tex]
∴ [tex]1.5=(1\frac{1}{300})^{12t}[/tex]
- Change the mixed number to an improper fraction
∴ [tex](1.5)=(\frac{301}{300})^{12t}[/tex]
- Insert ㏒ for both sides
∴ [tex]log(1.5)=log(\frac{301}{300})^{12t}[/tex]
- Remember [tex]log(a)^{n}=nlog(a)[/tex]
∴ [tex]log(1.5)=(12t)log(\frac{301}{300})[/tex]
- Divide both sides by [tex]log(\frac{301}{300})[/tex]
∴ 121.84 = 12 t
- Divide both sides by 12
∴ 10.155 = t
It takes 10.155 years until you have $3,000
Learn more:
You can learn more about the compound interest in brainly.com/question/4361464
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