Answer:
In about 14.21 years a certain amount will double if it attracts 5% interest rate compounded annually
Step-by-step explanation:
The formula for compound interest, including principal sum, is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where
∵ A certain amount is double in t years
- That means A is double P
∴ A = 2 P
∵ It attracts 5% interest rate compounded annually
∴ r = 5% = [tex]\frac{5}{100}[/tex] = 0.05
∴ n = 1 ⇒ compounded annually
- Substitute all of these values in the formula above
∵ [tex]2P=P(1+\frac{0.05}{1})^{(1)t}[/tex]
∴ [tex]2P=P(1.05)^{t}[/tex]
- Divide both sides by P
∴ [tex]2=(1.05)^{t}[/tex]
- Insert ㏑ for both sides
∴ [tex]ln(2)=ln(1.05)^{t}[/tex]
- Remember [tex]ln(1.05)^{t}[/tex] = t . ㏑(1.05)
∴ ln(2) = t . ㏑(1.05)
- Divide both sides by ㏑(1.05)
∴ 14.2067 = t
- Round it to the nearest hundredth
∴ t = 14.21 years
In about 14.21 years a certain amount will double if it attracts 5% interest rate compounded annually
