Question

Harrison and Sherrie are making decisions on their bank accounts. Harrison wants to put more money in as a principle amount because the more you start with, the more interest you will gain. Sherrie wants to put the original money in an account with a higher interest rate. Explain which method will result in more money.
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Answer 1

@TinkerbellGirl @texaschic101 @tkhunny

Answer 2

without any values to work with, either one could be best, at least thats what im seeing

Answer 3

Well this was the question

Answer 4

is the interest simple of compound? if compound we can develop a generality; let a be more principal, and b be higher interest

(P+a)(1+r)^n = P(1+(r+b))^n

Answer 5

is there a time, n, when these are equal? is there a time when they are not?

Answer 6

I wouldl have to assume that Harrison has also picked an account with a high interest rate. If so his plan would make the most money

Answer 7

hmmmm?

Answer 8

Can you explain Harrison's method

Answer 9

spose P = 1 for simplicity

(1+a)(1+r)^n = (1+(r+b))^n

divide both side by (1+r)^n

1+a = [(1+(r+b))/(1+r)]^n

simplify some stuff

1+a = [(1+b/(1+r) ]^n

a = [(1+b/(1+r) ]^n - 1

so we have a comparison when they should be equal, if ive done this right lol

Answer 10

what is this post responding to??? I'm really confused

Answer 11

is one method better than the other? well, since there are no concrete values to work with, we can setup a scenario in which both plans are equal for a given interval and use that to compare the plans

Answer 12

Ohh can you do it again but, this time explain it slower please I'm really trying to understand

Answer 13

its explained as slowly as you can read ....

Answer 14

one want to add more principal, the other want to add more interest

(P+a)(1+r)^n this adds 'a' to the principal

P(1+(r+b))^n this adds interest

is there a reasonable way in which for some given n, that the results are equal? if they are equal then one plan is not 'better' than the other

Answer 15

the principal is rather unimportant and we can assume it to be 1 for simplicity; as such

(1+a)(1+r)^n = (1+(r+b))^n

lets say we want the money to be in the account for 1 year, let n=1

(1+a)(1+r) = (1+(r+b))

now its just algebra ....

(1+a)(1+r) = 1+r+b

1+a = (1+r)/(1+r) + b/(1+r)

1+a = 1 + b/(1+r)

so when a = b/(1+r) they are the same

Answer 16

And Harrison method show better exponential growth of a function

Answer 17

the exponential growth is immaterial since we can conceive if a scenario for any time limit in which both plans would result in the same money value in the end.

Answer 18

spose they want to add .5 to the interest, let b = .5

a = .5/(1+r) for whatever the initial interest rate is

say r = .03; then the amount of money to add to the principal would be .5/1.03 ... in this case 1 + .49

Answer 19

go on

Answer 20

that was just adding some specifics

we can readily see that:

(1+.48)(1+.03) < 1+.5+.03

and

(1+.49)(1+.03) > 1+.5+.03

Answer 21

as such the added principle method is only limited by how much added principal you can apply. since we can always find some value that will best added interest for a given time period

Answer 22

I'm starting to get a better understanding

Answer 23

lets say we have 500 to invest for 20 years, at an initial rate of 5%

(P+a)(1+r)^n = P(1+(r+b))^n

(500+a)(1.05)^(20) = 500(1.05+b)^(20)

now, we can 'solve for a' for any given 'b' to determine when the plans are equal. knowing when they are equal, we can then determine for what values they are not equal

Answer 24

what this means is: either plan is fine since there is not concrete values to work with. one plan can be trumped by the other if we assume no limitations to what is added to principal or what is added to interest

Answer 25

and also assuming that 'better' means that for a given time frame, the results are comparable at the end of it all

Answer 26

so both methods are great it just depends on the principal rate and what is added to interest

Answer 27

thats a fair analysis. either plan can result in worse or better conditions; so it all depends on how you want to manage your money.

Answer 28

lets be absurd and say that the guy with added interest finds an account with 500% more interest. what should the other guy propose to best that?

(500+a)(1.05)^(20) = 500(1.05+b)^(20)

(500+a)(1.05)^(20) = 500(1.05+5)^(20)

500+a = 500(6.05/1.05)^(20)

a = 500(6.05/1.05)^(20) - 500

a = 8.13376...

let a = 8.14

Answer 29

might have to recheck some math ... but thats the idea

Answer 30

wait a sec I'm coming up with a final answer

Answer 31

8.13376 (10^17)

Answer 32

a = 813 376 303 973 522 261.6560 ...

let a = 813 376 303 973 522 261.66

:)

Answer 33

Make any corrections nessary

Answer 34

Harrison and Sherrie methods are both correct in a way because, it depends on the amount of principle added, or the amount of interest added. Both methods can be compared such that if Harrison adds more principle, then Sherrie can find an interest rate to match it. If Sherrie finds an interest rate, then Harrison can find an amount to add to the principle to best it. Either method is fine, and what is important is the financial goals that the money is spose to cover for, as well as the limitations that are inherent in a real world application to thier plans.

Answer 35

notice if we are realistic .... 500 principle, 20 year, interest of 5% compared to 8%

(500+a)(1.05)^(20) = 500(1.08)^(20)

then the amount of principle to add is about 378.333...

so adding 378.34 would produce something 'more' than the added interest

Answer 36

so the question is, do we have 379 laying about to invest? if not, then the added interest is best

Answer 37

I got it now whhhhooo hell yeah