Answer:
It will take about 27.7 years
Explanation:
* Lets talk about the compound continuous interest
- Compound continuous interest can be calculated using the formula:
A = P e^rt
• A = the future value of the investment, including interest
• P = the principal investment amount (the initial amount)
• r = the interest rate
• t = the time the money is invested for
- The formula gives you the future value of an investment,
which is compound continuous interest plus the principal.
- If you want to calculate the compound interest only, you need
to deduct the principal from the result.
- So, your formula is:
Compounded interest only = Pe^(rt) - P
* Now lets solve the problem
∵ The invest is $ 1000
∴ P = 1000
∵ The interest rate is 2.5%
∴ r = 2.5/100 = 0.025
- They ask about how long will it take to make double the investment
∴ A = 2 × 1000 = 2000
∵ A = P e^(rt)
∴ 2000 = 1000 (e)^(0.025t) ⇒ divide both sides by 1000
∴ 2000/1000 = e^(0.025t)
∴ 2 = e^(0.025) ⇒ take ln for both sides
∴ ln(2) = ln[e^(0.025t)]
∵ ln(e)^n = n
∴ ln(2) = 0.025t ⇒ divide both sides by 0.025
∴ t = ln(2)/0.025 = 27.7 years
* It will take about 27.7 years