Johan invests $4,000 at age 22 from the signing bonus of his new job. He hopes the investment will be worth $240,000 when he turns 66. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Round to the nearest tenth of a percent.
The interest rate needs to be 9.8% for the sum of $4000 to compound to $240,000
Since the interest compounds itself, hence the question concerns the compound interest.
Principal (Initial contribution)- $ 4000
Amount (Expected amount)- $ 240,000
Time period- investment started at 22 years and would continue until 66 years.
Time period= 66-22 years= 44 years
Rate of interest=
We know that for compound interest-
⇒Amount= principal (1+rate/100)ⁿ
Substituting the values if Amount, principal and time ("n") in the above equation
240,000= 4000 (1+rate/100) ⁴⁴
240,000/4000= (1+rate/100) ⁴⁴
Solving the above equation would yield us with the rate as 9.75% ≈ 9.8% (rounded off to tenth place after decimal)
Hence the Interest rate required by John would be 9.8%
Identify the variables of the formula:
t= 44 years (66-22=44)
Substitute the values into the formula
Solve for r. Divide each side by 4,000
Take the natural log of each side
ln60= ln e^44r
Use the power property and then simplify
ln60= 44r ln e
Divide each side by 44
Approximate the answer
r= 0.09305 ——> r= 9.3%
it would be see because your formula is f(x)=6x, so 6 times 1 is 6 and you go on and the best answer is c.