Question

Medal reward of course

Answer 1

Brooklyn has a goal to save $8,000 to buy a new entertainment system. In order to meet that goal, she deposited $4,132.79 into a savings account. If the account has an interest rate of 4.8% compounded quarterly, approximately when will Brooklyn be able to make the purchase?

10 years, 1 month

13 years, 10 months

14 years, 1 month

26 years, 10 months

Answer 2

uhhh
That's my name

Answer 3

Cjoens

Answer 4

jones*

Answer 5

Lol first name chris?

Answer 6

Is your first name Caitlyn? lol

Answer 7

LOL

Answer 8

Whew different first names WOhoo!

Answer 9

This is awesome I found a brother!!

Answer 10

I know the equation i just have a small question

Answer 11

Okay whats your quesh

Answer 12

whoa I cant its too hard..

Answer 13

P = 4, 132.79
F = 8, 000
i = 0.048
n = ? [solve for]

\[F = P( 1+i)^n\]

Answer 14

lol

Answer 15

lol its fine

Answer 16

@DemolisionWolf I thought the equation was A=P(1+r/n)^n(t)?

Answer 17

oh wait nvm i is r/t

Answer 18

ya, you can use that one.
they are basically the same.

use what you are comfortable with

Answer 19

but how do i turn years and months into one? thats what throws me off.

usually they are just one number so how do i turn the answers into one so i can plug them in?

Answer 20

A=P(1+r/t)^n(t)
r= 0.048
t = time in years?
n = number of times it is compounded in a year?

Answer 21

Its compounded quarterly so thats n i dont know how to get t though. I know i plug in the choices but i dont know how to solve it when its years and months... if it were just years or just months i could CONFUSING!! lol

Answer 22

ok,
so we can make it years.

to make it years, 'quarterly' means 4 times in a year. 4/12 = 0.25years. so you could plug in years as .25

Answer 23

t has to be one of these

10 years, 1 month

13 years, 10 months

14 years, 1 month

26 years, 10 months

Answer 24

@ganeshie8 could you help?

Answer 25

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

\(A = 8000\); \(P = 4132.79\); \(r = 4.8\% = 0.048\); \(n = 4\)


\(8000 = 4132.79\left( 1 + \dfrac{0.048}{4} \right)^{4t} \)

\(1.935738 = 1.012^{4t} \)

\(1.935738 = (1.012^4)^t \)

\(1.935738 = 1.0488709^t \)

Answer 26

Now convert each choice to decimal years:
10 years, 1 month = 10.08333 yrs
13 years, 10 months = 13.8333 yrs
14 years, 1 month = 14.083333 yrs
26 years, 10 months = 26.83333 yrs

Now use a calculator, and enter 1.0488709 raised to each number of decimal years in your choices to see which one is closest to 1.935738.

Answer 27

i know i shouldnt but i just took years and pluggerd them in and 13years was $7684.75 and 14 years was $8060.32

Answer 28

Use 13.8333 for 13 years and 10 months. Plug that in.
Then use 14.0833 for 14 years and 1 month. See what you get with thoses guesses for t.

Answer 29

I got 13.8333=$7996.45822 and 14.0833=$8092.42

Answer 30

Great.
The answer is 13.8333 years which means 13 years and 10 months.