Question

MEDAL!
Yvonne put $4,000 into a savings account. At the end of 3 years, the account had earned $960 simple interest. How many more dollars would she have in her account if the interest rate were 1% greater? Help Please!

Answer 1

@campbell_st

Answer 2

the interest rate is 8%

Answer 3

so 1st you need to find the rate of interest, so use the information you are given

formula is

I = Prn

you know I = 960, P = 4000 and n = 3

so

\[960 = 12000r~~~or ~~~r = \frac{960}{12000}\]

find r..

Answer 4

that will be a decimal value for r, multiply it by 100 to get the percentage value.

then add 1 to the answer

to find the extra money

use the new interest rate as a decimal in the formula with P still 4000 and n still 3

hope it helps

Answer 5

wait what formula do I use?

Answer 6

simple interest

I = Prn or I = Prt I = interest, P = Principal, r = interest rate as a decimal
n or t = time periods.

Answer 7

so like this? 960=1200*0.09

Answer 8

well.. we dunno what her interest rate is
thus, we'd want to know that first

thus \(\bf \qquad \textit{Simple Interest Earned}\\
I = Prt\qquad
\begin{cases}
I=\textit{interest earned}\to &\$960\\
P=\textit{original amount deposited}\to& \$4000\\
r=rate\\
t=years\to &3
\end{cases}
\\ \quad \\
960=4000\cdot r\cdot 3\impliedby \textit{solve for "r"}\)

Answer 9

well the thing is I already solved for the interest rate which is 8% and its telling me to add 1% to the interest rate (8%) which all together would be 9%.

Answer 10

right.... so.... you yes.. then you're correct is
\(\bf 960=1200*0.09 \)

then find the difference between both amounts

Answer 11

hmmm wait a sec....

Answer 12

we know the rate is 8% + 1% = 9%
we dunno what the earned interest is

so should just be \(\bf i=1200*0.09 \)

Answer 13

well... we're missing he years... so... hmm \(\bf i=1200*0.09 * 3\)

Answer 14

wait what do we need earned interest for?

Answer 15

and the years is the 3

Answer 16

well.. at 8%, on a principal of 12,000 over 3 years
she's got an earned interest of 960

so...you're asked

how much more, would she had now, had it been 9% instead of 8%?

so.... find how much is at 8%, we know that, 960
find how much is at 9%, we dunnno that

then get their difference

and that's how much she would have gottent more, had she been using 9% from the beginning

Answer 17

I am confused a little, can you set up the equation to plug In the 9% instead of the 8%?

Answer 18

hmmm actually, above I used 12,000, should have been 4000.... but anyway

just to clear that out

Answer 19

ok, can you show me the equation to find how much Yvonne will have in her account if she had 9% as her interest rate?

Answer 20

\(\bf \qquad \textit{Simple Interest Earned}\\
I = Prt\qquad
\begin{cases}
I=\textit{interest earned}\to &\$960\\
P=\textit{original amount deposited}\to& \$4000\\
r=rate\\
t=years\to &3
\end{cases}
\\ \quad \\
960=4000\cdot r\cdot 3\impliedby r=8\%
\\ \quad \\ \quad \\
I = Prt\qquad
\begin{cases}
I=\textit{interest earned}\\
P=\textit{original amount deposited}\to& \$4000\\
r=rate\to &0.09\\
t=years\to &3
\end{cases}
\\ \quad \\
I=4000\cdot 0.09\cdot 3\impliedby r=9\%\)

Answer 21

I=1080 but that cant be right if her total amount of money in her account is 4,960

Answer 22

1080 is the "earned interest" NOT her account total balance

is just the interest earned on the 4000, so the full balance of her account will be 4000+ 1080 at 9%

her total account balance will be 4000 + 960 at 8%

Answer 23

if you put $100 in the bank
and they pay you 10% after a year
that means the earned interest is 10% of 100, or $10

that doesn't mean you put in $100, and after a year you ended up with $10
or $90 less....

simply means, you started with 100, and now added 10 more to it, or 110

Answer 24

ok now im very confused, can you set up the equation that will show how much Yvonne will have in her account if she had 9% as her interest rate?

Answer 25

as clear as possible

Answer 26

hmm those are above... can't get clearer I'd think


do you even know what an earned interest amount is?

Answer 27

no, I had not learned about this yet

Answer 28

well... earned interest is amount extra, from the original amount

Answer 29

oh! wait I do know what it is I just forgot :p

Answer 30

you're asked
ok, she made 960 at what rate? you found 8%

so at 8% she made 960
at 9% she made how much?

what's the difference between the two amounts?

or

how much would she had made more, had she used 9% instead of 8%

Answer 31

I know but I don't know how to solve that, that is the reason why I asked this question

Answer 32

well.. how did you get the 8% for the rate?

you'd get the "i" for the 2nd rate of 9%, using the same "simple interest formula"

Answer 33

\(\bf \qquad \textit{Simple Interest Earned}\\
I = Prt\qquad
\begin{cases}
I=\textit{interest earned}\to &\$960\\
P=\textit{original amount deposited}\to& \$4000\\
r=rate\\
t=years\to &3
\end{cases}
\\ \quad \\
960=4000\cdot r\cdot 3\impliedby r=8\%
\\ \quad \\ \quad \\
I = Prt\qquad
\begin{cases}
I=\textit{interest earned}\\
P=\textit{original amount deposited}\to& \$4000\\
r=rate\to &0.09\\
t=years\to &3
\end{cases}
\\ \quad \\
I=4000\cdot 0.09\cdot 3\impliedby r=9\%\)

Answer 34

I got 8% for the rate by using the formula to find the rate --- A=1/P*T *100

Answer 35

well... you got 1080 already from the 9%, right?

so.. we know at 8% she earned 960
we also know at 9% she earned 1080

so 1080 - 960 = " how much MORE she would have gotten, had she used 9%"

Answer 36

ok now this makes much more sense