35.8k views
5 votes
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?

User Cliu
by
7.1k points

1 Answer

3 votes

Answer:

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

User Adomas Baliuka
by
6.8k points