Question

You invest $1,600 in an account that pays an interest 6.5%, compound continuously. Calculate your balance after 6 years. Round to the nearest hundredth.

Answer 1

Can anyone show me step by step on how to do this, like if you were explaining this to a 5 year old because I am clueless to Exponential and Logarithmics!

Answer 2

6.5 % interest compounded continuously
= (e^r) -1
= (2.718181828^ .065) -1
=1.0671590244 -1
=.0671590244
=6.71590244 % compounded continuously

Answer 3

But how did you get (2.718181828^ .065) What did you do to get those numbers?

Answer 4

Okay I went to this web page
http://www.1728.org/rate.htm
and used the 3rd formula on that page
'e' is the base of natural logarithms 2.718281828

Yes, I know that's a lot for a 5 year old but I'll try to explain what you need to know.

Answer 5

What do you mean by base of natural logarithms?
Sort of like how Pi = 3.14?

Answer 6

Compounded interest is tough enough to explain but what intructor gives you a CONTINOUSLY compounded interest problem?

Answer 7

Let's just act if this were a compounded interest problem

Answer 8

The formula for the total of a compounded interest account is

TOTAL = Principal * (1 + rate)^years

(Page explaining compound interest is here: http://www.1728.org/compint2.htm)

Answer 9

The question does show this formula but, idk how to apply it and then solve.

Answer 10

1,600.00 invested 6 years at 6.5%

TOTAL = principal * (1+rate)^years
TOTAL = 1,600.00 * (1.065)^6
TOTAL = 1,600.00 * (1.4591422965)
TOTAL = 2,334.63

What formula did they tell you?

Answer 11

A = Pe^rt ??

Answer 12

Okay
TOTAL = Principal * e^(rate * time)
TOTAL = 1,600 * 2.718281828 ^ (.065 * 6)
TOTAL = 1,600 * 1.4769807938
TOTAL = 2,363.17

Answer 13

Wait, how do I calculate 2.718281828 ^ (.065 * 6) to get 1.4769807938? Like 2.7182 0.65, I'm still doing it wrong. :(

Answer 14

I guess I first should have shown you this calculation
.065 * 6 = 0.39
Then next we calculate
e^.39
or
2.718281828 ^ .39

Answer 15

I got 1.06012991292 ?? instead of 1.4769807938

Answer 16

You are raising a number to a power on your calculator, correct?

Answer 17

I'm using the standard calculator in my laptop, Sorry I'm so dumb, online math class is so difficult for me and I miss having a teacher face to face.

Answer 18

Yeah, even that formula you posted A = Pe^rt doesn't really explain anything does it?

Answer 19

This one is different concerning this formula A = p(1 + r)^t
Tina Invests $1,000 with interest rate 6.75%
How many years will it take for the account to reach $18,600 ?

Answer 20

Hopefully I can understand these ones better than A = Pe^rt

Answer 21

Hi LadyLillyz I'm back

Answer 22

I'm still here!

Answer 23

First, let's see if you can raise a number to a power.

Do you know how to calculate this?
2^3

Answer 24

Yes, you could just calculate 2 *2 * 2 but can you do it with your calculator?

Answer 25

Negative.

Answer 26

Any other possible sources via online calculators?

Answer 27

You don't know how to raise a number to a power?
You'll DEFINITELY need to know that in order to do these problems.
Let me see about online calculators.

Answer 28

Here's one right here:
http://www.1728.org/calc.htm

Answer 29

I do know how to raise a number to a power, just not the complicated one like we did previously "2.718281828 ^ .39"

Answer 30

Okay go here but fore you do
http://www.1728.org/calc.htm
try raising 2 to the third power
2^3 = ?

Answer 31

It is 8

Answer 32

You used the calculator right?

Answer 33

I used the calculator after raising it like you asked.

Answer 34

Okay - now to get more accuracy out of that calculator, go to the bottom of that page and change the 5 to a 20

Answer 35

Objective done.

Answer 36

Now just to see if it changed try 2^.5

Answer 37

You should get 1.4142135623730951

Answer 38

1.4142135623730951, 100% match

Answer 39

All right we are set to do some continuously compounded interest problems!!!

Answer 40

Okay why not try 2.718281828 ^ .39

Answer 41

1.4769807937853678,

Answer 42

Well, now you know how to raise a number to a power.
Now if you look way back to where that had to be calculated, now you know where I got that number.
If not I'll just type it all again.

Answer 43

Here's the original problem:

TOTAL = Principal * e^(rate * time)
TOTAL = 1,600 * 2.718281828 ^ (.065 * 6)
TOTAL = 1,600 * 2.718281828 ^ (.039)
TOTAL = 1,600 * 1.4769807938
TOTAL = 2,363.17

Answer 44

Okay, it's getting easier now, but the other question earlier, with a different formula and a different question..Tina Invests $1,000 with interest rate 6.75%
How many years will it take for the account to reach $18,600 ? It doesn't state x amount of money after years but instead, the opposite?

Answer 45

1,000 rate =6.75
when does it reach $18,600?
Is this continuously compounded?

Answer 46

It gives me a formula A = P(1 + r)^t

Answer 47

That's what your book says? Okay well that is regular compound interest.
But that has to be solved for 't'.
If you can't find that formula I'll show you how to do it.

Answer 48

I don't want to force you to give me a full lecture and waste your time, I think 1 more solid example and good explaination I can do other problems independently, but I do come across another speed bump, I will notify you.

Answer 49

TOTAL = principal * (1 + rate)^t

TOTAL / principal = (1 + rate)^t
take logarithms of both sides
log (TOTAL / Principal) = time * log (1 + rate)

time = log (TOTAL / Principal) / log (1 + rate)

time = log (18,600 / 1,000) / log (1.065)

time = 44.751767801

(Okay I left out all the log calculations)

Answer 50

I'd say THIS problem was a speed bump
unless you think you could have solved the formula for time. LOL