Question

HI AGAIN
Candice deposited $3,587.39 into a savings account with an interest rate of 4.2% compounded twice a year. About how long will it take for the account to be worth $5,000?

Answer 1

@jim_thompson5910 hi

Answer 2

now you use a similar formula

Answer 3

A = P(1+r/n)^(n*t)

in this case

A = 5000
P = 3587.39
r = 0.042
n = 2 (compounding 2 times a year)
t = unknown

plug all that in and solve for t

Answer 4

i hate solving for crap algebraically, it makes my head bleed...

Answer 5

well this is an algebra class (sounds like it?) so that's to be expected

the solving part, not head bleeding part

Answer 6

i know lol

Answer 7

im trying

Answer 8

ok tell me what you get

Answer 9

i got this far\[1412.61=(1.021)^{2timest}\]

Answer 10

how are you getting 1412.61?

Answer 11

subtracting 3587.39 from 5000

Answer 12

its probably soooooo wrong

Answer 13

oh...you don't subtract

you're actually dividing

Answer 14

thats why im here

Answer 15

close though

Answer 16

yeah that's why it's best to show any/all work you can

Answer 17

ummmmm... i dont know what to do

Answer 18

so i divide what?

Answer 19

5000 = 3587.39(1.021)^(2*t)

divide both sides by 3587.39

Answer 20

i dont have a texas instrument calculator, i have a phone

Answer 21

just do 5000/3587.39 and tell me what you get

Answer 22

i cant do this on my phone

Answer 23

i can do that

Answer 24

btw you shouldn't be doing this on a phone lol

you need a real calculator

Answer 25

i know, my friend had to borrow mine haha

Answer 26

google or wolfram alpha are good choices

example

if you typed in "5000/3587.39" without quotes into google, you would get

https://www.google.com/search?hl=&q=5000%2F3587.39&sourceid=navclient-ff&rlz=1B3GGLL_enUS420US420&ie=UTF-8

Answer 27

or you can use calculators for the computer (like graphcalc)

Answer 28

and i got 1.39 for 5000/3587.39

Answer 29

cool, didnt know that

Answer 30

yeah roughly 1.39377, good

Answer 31

so 1.39377 = (1.021)^(2*t)

Answer 32

okay

Answer 33

how do you isolate t?

Answer 34

dang man, i forget, i havent taken algebra since sophomore year, im a senior

Answer 35

so it's been 2 years

Answer 36

i probably sound really stupid haha

Answer 37

that's a long time

Answer 38

nah not really

Answer 39

yeah, haha

Answer 40

like i said, it's about practice

Answer 41

well you would use logs to isolate t

Answer 42

sound familiar?

Answer 43

OMG... all i remember is i HATED logs

Answer 44

yeah they are a pain at first

Answer 45

you apply the log to both sides to get


1.39377 = (1.021)^(2*t)


log( 1.39377 ) = log( (1.021)^(2*t) )

Answer 46

that allows you to pull down the exponent like so

log( 1.39377 ) = 2t*log( 1.021 )

Answer 47

on the left: .14419111 roughly

Answer 48

then you divide both sides by 2*log(1.021) to get


log( 1.39377 ) = 2t*log( 1.021 )


log( 1.39377 )/(2*log( 1.021 )) = t


t = log( 1.39377 )/(2*log( 1.021 ))


t = ??

Answer 49

yeah you could evaluate each log one at a time like that

Answer 50

how would you figure out the right side?

Answer 51

divide both sides by 2*log(1.021)

Answer 52

to isolate t

Answer 53

how would i plug it in to a calculator?

Answer 54

evaluate 2*log(1.021) to get _____

Answer 55

then you divide .14419111 by that result

so .14419111/(whatever you got)

Answer 56

i got 2.042

Answer 57

for the right side

Answer 58

hmm something went wrong

Answer 59

you just doubled 1.021 by mistake

Answer 60

and forgot about the log

Answer 61

i did 2*log(1.021)

Answer 62

you left off the log though i think

Answer 63

possibly, let me do it again

Answer 64

ok

Answer 65

.31005573?

Answer 66

no

Answer 67

https://www.google.com/search?q=2*log%281.021%29&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a&channel=rcs

Answer 68

UGHHHHH FRUSTRATION with myself

Answer 69

its fine, as long as you can spot where you went wrong

Answer 70

i did, i just put it in the calculator wrong

Answer 71

i gotcha

Answer 72

i got 7.98778888

Answer 73

me too

Answer 74

so about 8 years

Answer 75

but there are these two choices that are very close

Answer 76

which ones

Answer 77

8 years 0 months

8 years, 1 month

Answer 78

the most accurate I get the answer to be is 7.987787029

Answer 79

it would just be 8 years, cause it just barely makes 8 years

Answer 80

that rounds to 8 years

you could go another month, but that will definitely be over $5,000

Answer 81

okay thanks again man

Answer 82

np