It will take 12.8047 years for Jari's investment to double
Step-by-step explanation:
The formula for compound interest, including principal sum is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where:
Jari invests in a CD with an annual interest rate of 5.45% compounded quarterly. We need to find how many years it will take for Jari's investment to double.
∵ The annual interest rate is 5.45%
∴ r = 5.45% = 5.45 ÷ 100 = 0.0545
∵ The interest rate is compounded quarterly
∴ n = 4
∵ The Jari's investment is doubled in t years
∴ A = 2P
- Substitute these values in the rule above
∵ [tex]2P=P(1+\frac{0.0545}{4})^{4t}[/tex]
- Divide both sides by P
∴ [tex]2=(1+\frac{0.0545}{4})^{4t}[/tex]
∴ [tex]2=(1+0.013625)^{4t}[/tex]
∴ [tex]2=(1.013625)^{4t}[/tex]
- Insert ㏒ to both sides
∴ [tex]log(2)=log[(1.013625)^{4t}][/tex]
- Remember [tex]log(a)^{n}=nlog(a)[/tex]
∴ ㏒(2) = 4t ㏒(1.013625)
- Divide both sides by 4 ㏒(1.013625) to find t
∴ t = 12.8047 years
It will take 12.8047 years for Jari's investment to double
Learn more;
You can learn more about compound interest in brainly.com/question/4361464
#LearnwithBrainly
