1. ## Investment

An investment advisor is planning the retirement of a customer. The customer has $10,000 dollars to invest and needs the investment to increase to$30,000 within 20 years...so 20 years or less.

Now I need to figure out 2 investment plans to make the above numbers work themselves out. I am so incredibly frustrated. I thought of the compound interest formula, but the problem does not tell me how many times a year the investment can or should be compounded.

Can someone please shed some light? I really need help!

2. $\displaystyle A=P\left(1+\frac{r}{100}\right)^t$

$\displaystyle 30,000=10,000\left(1+\frac{r}{100}\right)^{20}$

solve for r to find the required interest rate.

3. Also

$\displaystyle I+P = \frac{PRT}{100}+P$

$\displaystyle 20,000+10,000 = \frac{10,000\times R\times 20}{100}+10,000$

once again solve for R to find required rate using simple interest.

4. I have been told to use the formula A = Pe^rt.

So, I get $30,000 =$10,000 e^20r

I am unsure where to go from here????

5. OK, I think I got it. I got a percentage of 5.5%.

Can anyone tell me if this is correct?

6. Originally Posted by missyd819
I have been told to use the formula A = Pe^rt.

So, I get $30,000 =$10,000 e^20r

I am unsure where to go from here????
$\displaystyle 30000 = 10000e^{20r}$

divide both sides by 10000 ...

$\displaystyle 3 = e^{20r}$

take the natural log of both sides ...

$\displaystyle \ln(3) = 20r$

$\displaystyle r = \frac{\ln{3}}{20} \approx 0.055$ or 5.5%

now the big question ... do you know what the formula $\displaystyle A = Pe^{rt}$ means?

7. YESSSS! I got the 5.5% too. I figured it out. Sooo proud of myself!!

I believe it means the money is continuously compounded.

8. Originally Posted by missyd819
YESSSS! I got the 5.5% too. I figured it out. Sooo proud of myself!!

I believe it means the money is continuously compounded.
correct

9. ## Investment

Hi, I have noticed that this problem was already posted one time here, however even after reading I am still not clear on the investment plan part.
The problem states: create three investment plans for customer who has $10,000 dollars to invest and needs the investment to increase to$30,000 dollars within 20 years.
I have created a plan using Exponential Growth formula for a long term CD investment, and a Compound Interest Formula for a savings account. Now I am not sure what to use for the third plan . Anyone? I was thinking about investing in stocks with dividents for 20 years, however not sure what formulas to apply and how. Please Help!!

thank you

10. The poor guy wants to invest $10,000 and get back$30,000
20 years later; he doesn't care HOW it's done: so why all the
run around about 3 plans?
10000(1 + i)^20 = 30000
ONLY one annually compounded rate is possible.

11. How did you use the Exponential Growth formula?

I used continuous and I also found a plan on the Fidelity website that met the criteria for this plan. I need to use something else besides continuous growth, but I am unsure how to solve this using exponential growth.

Thanks.