Question

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

Answer 1

15.7 years

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 + (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 + (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`)

`(log 3)/(log 1.005833) = 12t`

`(0.4771212547)/(0.0025258801) = 12t`

`188.89307 = 12t`

Therefore
`t` = 15.7 years