Question

A principal of $4000 is invested at 8.75% interest, compounded annually. How many years will it take to accumulate $14,000 or more in the account?

Answer 1

The number of years will it take to accumulate the amount in the account is 15 years .

Explanation:

Given as :

The principal invested = p = $4000

The rate of interest = r = 8.75% compounded annually

The amount accumulate after t years = A = $14,000

Let The years of accumulation = t years

From Compounded Interest

Amount = Principal ×
`(1+(\textrm rate)/(100))^(\textrm time)`

Or, A = p ×
`(1+(\textrm r)/(100))^(\textrm t)`

Or, $14000 = $4000 ×
`(1+(\textrm 8.75)/(100))^(\textrm t)`

Or,
`(14000)/(4000)` =
`(1.0875)^(\textrm t)`

Or, 3.5 =
`(1.0875)^(\textrm t)`

Taking log both side

`Log_(10)`3.5 =
`Log_(10)`
`(1.0875)^(\textrm t)`

Or, 0.54 = t
`Log_(10)`1.0875

or, 0.54 = t × 0.036

∴ t =
`(0.54)/(0.036)`

I.e t = 15

So, The number of years will it take = t = 15 years

Hence, The number of years will it take to accumulate the amount in the account is 15 years . Answer