Question

A principal of $4200 is invested at 3.5% interest, compounded annually. How many years will it take to accumulate $7000 or more in the account?

Answer 1

15 years.

Explanation:

We have been given that a principal of $4200 is invested at 3.5% interest, compounded annually. We are asked to find the time it will take for the amount to be $7000 or more.

We will use compound interest formula to solve our given problem.

`A=P(1+(r)/(n))^(nt)`, where,

A = Final amount,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year,

t = Time in years.

`3.5\%=(3.5)/(100)=0.035`

Substitute given values in above formula.

`7000=4200(1+(0.035)/(1))^(1*t)`

`7000=4200(1+0.035)^(t)`

`7000=4200(1.035)^(t)`

`(7000)/(4200)=(4200(1.035)^(t))/(4200)`

`1.6666666=1.035^t`

`1.035^t=1.6666666`

Take natural log on both sides:

`\text{ln}(1.035^t)=\text{ln}(1.6666666)`

`t\cdot \text{ln}(1.035)=\text{ln}(1.6666666)`

`t\cdot 0.0344014267173324=0.5108255837659899`

`t=(0.5108255837659899)/(0.0344014267173324)`

`t=14.848965`

`t\approx 15`

Therefore, it will take 15 years to accumulate $7000 or more in the account.