Question

Please help me with this! What principal invested at 12% compounded continuously for 4 years will yield $1470? Round the answer to two decimal places.

a. $2375.63
b. $1468.38
c. $562.85
d. $909.61

Answer 1

Have you considered evaluating: \(1470 = Deposit\cdot e^{0.12\cdot 4}\)

I do hope it is obvious that the first two are no good. (a) is just silly. (b) is too close.

Answer 2

Principal = Total / (1 + rate)^years

Answer 3

Okay, thank you guys!

Answer 4

I got 909.61!

Answer 5

Is that right?

Answer 6

cats - I'm looking for a formula for continuously compounded interest - be juat a few minutes.

Answer 7

If you didn't do anything wrong deliberately, there is a good chance you got it right. What do you think? Did you get it right?

Answer 8

Great! I think I got it right, thanks for the help guys!

Answer 9

Perfect. A little confidence goes a long way. Good work.

Answer 10

I got the formula
continuously compounded interst rate = e^(annual rate) -1
where e = 2.718281828
so 12% continuously =
((2.718281828)^.12)-1
=.1274968516

Answer 11

Okay, thank you so much! =)

Answer 12

I've got the formula worked out too.
Principal = Total / (1 + rate)^years
Principal = 1,470 / (1.12)^4
Principal = 909.61

Here's a handy calculator to check your work:
http://www.1728.org/compint.htm

Answer 13

Great, thanks for all the help!

Answer 14

Thank you :-)

Answer 15

Ummm.... \(\dfrac{1470}{1.12^{4}} = 934.22 \ne 909.61\) is Annual Compounding

Seemed kind of magic, up there. Had you used the rather silly .1274968516.

Seriously, just use the exponential functions. There is absolutely no need to convert to annual interest.