An investment service promises to triple your money in 12 years. Assuming continuous compounding of interest, what rate of interest is needed?
For the question is it asking me if simple interest or continuously compounded interest is needed?
Or
Is it asking for a number in the rate of interest like .06 ?
Also, would anyone know which equation I should use? 1) Exponential Growth
2) Af=A0((1)+(r/n))^nt
3) A=Pe^rt
I think it's A=Pe^rt (Continuous Growth) or maybe Af=A0((1)+(r/n))^nt (Compound Interest)
Also could anyone type in the answer they got.
Thank You.
Investment companies usually do not deal in continuous compounding of interest, usually they are quoted as compounded annually, compounded semi-annually, compounded monthly or something like that.
let's assume an annual interest rate, so we would have
3 = (1+i)^12
take 12th root of both sides
3^(1/12) = 1+i
1+i = 1.09587
i = .09587 or 9.587% per annum
for continuous growth
3 = e^(12r)
12r = ln3
r = ln3/12 = .09155 or 9.155%
Oh, so you want to triple your money in 12 years? That's quite ambitious! But don't worry, I'm here to help you with a touch of humor.
First, let's clarify what the question is asking. It wants you to find the rate of interest needed to triple your money in 12 years using continuous compounding. So, it's not simple interest – we're getting fancy with continuous compounding here.
As for which equation to use, I'm sorry to burst your bubble, but none of the options you mentioned seem quite right. We need to use the equation for continuous compounding, which is:
A = Pe^(rt)
Where:
A = the final amount (triple your initial investment)
P = the principal (your initial investment)
e = the mathematical constant approximately equal to 2.71828
r = the annual interest rate (what we need to find)
t = the time in years (12 years in this case)
Since we want to triple our money, we can set A = 3P. Now, rearrange the equation to solve for r:
3P = Pe^(rt)
Divide both sides by P:
3 = e^(12r)
Take the natural logarithm of both sides:
ln(3) = 12r
Finally, divide both sides by 12:
r = ln(3)/12
Now, you can bust out your calculator to find the numerical value of ln(3)/12, which will give you the rate of interest needed to triple your money in 12 years using continuous compounding. Best of luck with your investment, my financially curious friend!
Based on the given information, the question is asking for the rate of interest needed in continuously compounded interest. In other words, it wants to know the interest rate that, when compounded continuously, will result in tripling your money in 12 years.
To answer this question, you can use the formula A = Pe^rt, where:
- A is the future value (triple the initial investment)
- P is the initial investment
- e is a mathematical constant approximately equal to 2.71828
- r is the interest rate
- t is the time period in years
Let's assume you start with an initial investment of P. After 12 years, the future value A would be three times the initial investment (3P).
Therefore, the equation becomes:
3P = Pe^(r * 12)
To solve for the rate of interest r, we can simplify the equation by canceling out P:
3 = e^(r * 12)
To isolate r, we can take the natural logarithm (ln) on both sides of the equation:
ln(3) = r * 12
Now, you can solve for r by dividing both sides of the equation by 12:
r = ln(3) / 12
Using a calculator to evaluate ln(3) and dividing it by 12 will give you the rate of interest needed to triple your money in 12 years when compounded continuously.