## anonymous 5 years ago If I want to know what is 20200/e(0.07695)(16), how do I input the "e" in the calculator?

1. anonymous

I understand the e = ln but Im not getting the same anwer my instructors gets

2. anonymous

the problem is A=pe^rt, where A=20200/e(0.076950(16) his answer is 5897.23

3. anonymous

The r =7.695% t= 16 years) or 16. I need help with finding e, please

4. anonymous

Hi, do you have any idea how to solve this?

5. nowhereman

e is Euler's constant at about 2.71828. A good calculator should have it stored. It is the following limit: $e = \lim_{n→∞}{(1+1/n)^n} = \sum_{n=0}^∞{\frac{1}{n!}}$$= 1 + 1\left(1+\frac 1 2 \left(1 + \frac 1 3\left(1+\frac 1 4\left(1+\frac 1 5\left(1 + \cdots\right)\right)\right)\right)\right)$

6. anonymous

That looks like stats. Would the same be applied to basic algebra?

7. nowhereman

It has nothing to do with statistics. Euler's constant is one of the most basic (next to π) constants of mathematics. It occurs very often, especially in analysis.

8. anonymous

That method is not getting me the same answer as my instructor

9. nowhereman

Well, the only way I can get a nearly equal is by calculating $\frac {20200}{1.08^{16}}$ But that is not really accurate if you are talking about interests. Then I would do $\frac{20200}{1.07695^{16}} = 6169.11$

10. anonymous

Here's the entire question: what principal should be deposited at 7.695% to ensure the acct will be worth $20200 in 16 years. I have 2020/e(0.07695)(16) 11. anonymous The formula is A=pe^rt. Im not understanding "e" and its throwing my answer off. His answer is$5897.23

12. anonymous

In this case do you know how to calculate the e?

13. nowhereman

That formula looks strange. Lets say initially you deposit a, and you have an interest rate of r = 7.695% = 0.07695 then after the first year you have your initial amount PLUS the interest: $a_1 = a + r\cdot a = a\cdot (1 + r)$ and one year later the same is true based on a1. So after n years you get $a_n = a\cdot(1+r)^{n}$ No e there.

14. anonymous

Do you know how he got \$5897.23?

15. nowhereman

I told you above. He rounded the interest rate to 8% and used the correct formula $a = \frac{a_n}{(1+r)^n}$ at least that is the closest I can come to that solution.

16. anonymous

In this case A = 20200/1+16?

17. anonymous

20200/(1+(0.07695)(16)?

18. anonymous

You have to use $$A = Pe^{rt}$$ When doing continuously compounded interest. e is the base of the exponential function. You should have a button on your calculator for it (typically it's the same button as the LN button). And if not you can use an approximate value of 2.71828183