Question

2000 is invested at 7% annual interest, compounded monthly. When will the balance triple?

Answer 1

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

$FV = P ( 1 + \frac{r}{n} ) ^1^2^t$

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

$6000 = 2000 (1 + \frac{0.07}{12} )^1^2^t$

$6000 = 2000 (1.005833 )^1^2^t$

Dividing both sides of the equality sign would give us

$3 = 1.005833^1^2^t$

Taking ㏒ of both  sides of the equality sign

㏒($3$) = ㏒($1.005833^1^2^t$)

㏒($3$)  = ($12t$) (㏒$1.005833$)

$\frac{log 3}{log 1.005833} = 12t$

$\frac{0.4771212547}{0.0025258801} = 12t$

$188.89307 = 12t$

Therefore $t$ = 15.7 years