Answer:
15.7 years
Step-by-step explanation:
Since we were asked how much it would take the principal (2000) to be tripled, we would triple it i.e 2000 × 3 = 6000
To find the time required, t, we would be making use of the equation below
[tex]FV = P ( 1 + \frac{r}{n} ) ^1^2^t[/tex]
Where FV is the tripled principal
P is the Principal = 2000
r is the percentage Interest = 7% i.e 0.07
n is the number of months that the principal is deposited I.e annually = 12 months
Fixing in the parameters, we have
[tex]6000 = 2000 (1 + \frac{0.07}{12} )^1^2^t[/tex]
[tex]6000 = 2000 (1.005833 )^1^2^t[/tex]
Dividing both sides of the equality sign would give us
[tex]3 = 1.005833^1^2^t[/tex]
Taking ㏒ of both sides of the equality sign
㏒([tex]3[/tex]) = ㏒([tex]1.005833^1^2^t[/tex])
㏒([tex]3[/tex]) = ([tex]12t[/tex]) (㏒[tex]1.005833[/tex])
[tex]\frac{log 3}{log 1.005833} = 12t[/tex]
[tex]\frac{0.4771212547}{0.0025258801} = 12t[/tex]
[tex]188.89307 = 12t[/tex]
Therefore [tex]t[/tex] = 15.7 years