Question

Use the compound interest formulas A = Pert and A = P(1+r/n)^nt to solve.

Suppose that you have $11,000 to invest. Which investment yields the greater return over 10 years: 6.25% compounded continuously or 6.3% compounded semiannually?

Answer 1

A. $11,000 invested at 6.25% compounded continuously over 10 years yields the greater return.
B. Both investment plans yield the same return.
C. $11,000 invested at 6.3% compounded semiannually over 10 years yields the greater return.

Answer 2

Well for your compounded continuously option, we just plug in the numbers into the A =Pe^(rt) formula. P is your principal, your initial amount, so 11,000. Rate is your percentage written as a decimal, so .0625 and time is 10. This gives us this equation:
\[A = 11000e ^{(10)(.0625)}\] For the second equation, r is again written as a decimal, but is .063 this time. Time is still 10 years. N is the amount of times the interest is compounded each year. So semi-annually means twice a year, meaning n = 2. So if we plug the numbers into that formula, we get:
\[A = 11000(1 + \frac{ .063 }{ 2 })^{(2)(10)}\]
Now you just need to do the calculator work and see which yields the greater return :3

Answer 3

whats the "e" in the first equation?

Answer 4

e is a number kinda like pi.

Answer 5

2.71...

Answer 6

It stands for exponential function. It's the inverse of the log function. Where it actually comes from is:
\[\lim_{n \rightarrow \infty}(1+\frac{ 1 }{ n })^{n}\]
A calculus concept, but yeah....2.72blah blah.

Answer 7

well for 1. i got 335.637 without doing the e or whatever
for 2. i got 1.250^81

Answer 8

You need to calculate the e, though. e is a number that must be calculated. You're taking e to a certain power in the first equation. For #2 you should get something like 20454.

Answer 9

Your calculator should have a button like
\[e ^{x} \] on it somewhere

Answer 10

ok i see it

Answer 11

Yep. So we need to do e^(.625) and then multiply that result by 11000.

Answer 12

for one i got 20550.70553

Answer 13

That sounds right ^_^
Now see if you can do it correctly for the 2nd one.

Answer 14

i got 21887.67749

Answer 15

Hmm...Wonder why you're getting that. Probably the order of operations make it harder on youf or your calculator.

Answer 16

So let's do this piece by piece then, starting with inside of the parenthesis. So if I only do:
\[1+\frac{ .063 }{ 2 }\], you should get 1.0315, correct?

Answer 17

yes!

Answer 18

Awesome. Now take that to the 20th power.

Answer 19

1.859450605

Answer 20

Multiply by 11000.

Answer 21

20453.95666

Answer 22

Much better :P So you can see which one is larger now :3

Answer 23

lol sorrry :p and yes the first ((:

Answer 24

Yeah, so there ya go :3

Answer 25

thankk yaa once again !

Answer 26

yep yep :3