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

Answer:

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

Step-by-step 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 × $(1+\dfrac{\textrm rate}{100})^{\textrm time}$

Or, A = p × $(1+\dfrac{\textrm r}{100})^{\textrm t}$

Or, $14000 = $4000 × $(1+\dfrac{\textrm 8.75}{100})^{\textrm t}$

Or, $\dfrac{14000}{4000}$ = $(1.0875)^{\textrm t}$

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 = $\dfrac{0.54}{0.036}$

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