Question

Carrie deposited $5,288.73 into a savings account with an interest rate of 2.3% compounded quarterly. About how long will it take for the account to be worth $8,000?

18 years, 10 months

18 years, 1 month

16 years, 5 month

18 years, 2 months

Answer 1

A formula for calculating annual compound interest is
A = P \left(1 + \frac{r}{n}\right)^{nt}
where
A = value after t periods
P = principal amount (initial investment)
r = annual nominal interest rate (not reflecting the compounding)
n = number of times the interest is compounded per year
t = number of years the money is borrowed for

Answer 2

\[8000 = 5288.73( 1+\frac{ i }{ 4 })^{4x}\]

solve for x

Answer 3

plug in what you know and solve the missing letter

Answer 4

@mebs thats how :)

Answer 5

AHHHH yea =)) @mary.rojas

Answer 6

@mebs isnt there something special you have to do to solve for x in this case

Answer 7

like ln or log or something

Answer 8

So D?

Answer 9

Ohh yea we could do that good idea but \[\sqrt[4]{ }\]

is a better idea...

Answer 10

Actually your right @mary.rojas you have to do ln1.51265 =4xln(whatever)

Answer 11

Wait no, it's 16 years and 2 months. That's what I got with the formula you said

Answer 12

leme check

Answer 13

yeahh i forgot how to do that. but you can plug each choice in for x until you get the desired amount.

Answer 14

Its 18.04

Answer 15

18.04? That isn't a choice

Answer 16

its in years

Answer 17

18 years and 4 months??? That still isn't a choice

Answer 18

Not 4 months

Answer 19

its 18 years and 1 month....

Answer 20

You round it... 0.0457333 * 12 = 0.5476 = ~~1....

Answer 21

1 month divided by 12 months equals 0.08333 so 18 years and 1 month is equal to 18.08333333

Answer 22

Just pick the closest one...

Answer 23

\(A = P \left(1 + \frac{r}{n}\right)^{nt}\)

\(8000 = 5288.73 \left(1 + \dfrac{0.023}{4}\right)^{4t}\)

\(1.51265 = \left(1.00575 \right)^{4t}\)

\( \log {1.51265} = \log{\left(1.00575 \right)^{4t} }\)

\(0.179739 = 4t \log{1.00575 }\)

\(72.18297 = 4t\)

t = 18.05 ~years

\( 0.05 ~years \times \dfrac{12 ~months}{1 ~year} = 0.55 ~months \approx 1 ~month\)

Answer: 18 years and 1 month

Answer 24

yayyy! @mathstudent55

Answer 25

That's what i am talking about!! @mathstudent55 @mary.rojas

Answer 26

Thank you all! Wish I could give 3 medals, but I can't haha

Answer 27

:)

Answer 28

your welcome =))

Answer 29

Do any of you know how to find monthly payments? I'm making a separate question for it, if you know how please help! x.x

Answer 30

@mebs did it correclty and before me. He deserves a lot of credit and the medal I gave him.

Answer 31

the monthly payment formula..

\[P = R \frac{[( 1-(1+\frac{ i }{ n })^{-nt} ]}{ \frac{ i }{ n } }\]

Answer 32

Thanks haha @mathstudent55

Answer 33

You can also use..

\[M= \frac{ P \times i }{ (c)[(1-(1+\frac{ i }{ c) })]^{-nc} }\]

Answer 34

I'm not sure what I'm doing wrong, I've plugged everything in but i'm getting a large number

Answer 35

well how large is it? and what are you investing is it compounded yearly and what were you expecting... Best thing to do is to repost this as a new question...

Answer 36

Rita owes $9,739 on a credit card with a 21.5% interest rate compounded monthly. What monthly payment should she make to pay off this debt in six years, assuming she does not charge any more purchases with the card?

Answer 37

Is $20.15 an option. ...

Answer 38

No

Answer 39

$909.17

$135.26

$241.82

$2,093.89

Answer 40

its 241082

Answer 41

$241.82 yea my bad not 241082

Answer 42

\[\frac{ 9739 \times 0.215 }{[ (12)(1-(1+0.017916666)^{-72}] }\]

try that on ur calculator

Answer 43

8.6588 ?? Idk

Answer 44

no try again.. you should get 241.82

Answer 45

\( M = \dfrac{rP}{1 - (1 + r)^{-n} } \)

where M = monthly payment
r = annual rate divided by 12 and expressed as a decimal
n = number of months

\( M = \dfrac{0.01791667 \times $9739}{1 - (1 + 0.01791667)^{-72} } \)

\( M = \dfrac{$174.4904}{1 - 0.2784324 } \)

\( M = \dfrac{$174.4904}{0.7215676} \)

\(M = $241.82 \)

Answer is C.