Question

More Financial Algebra help!

Every six months, Jessa deposits $525 into an interest-bearing account to save for her children’s tuition. The interest rate on the account is 5.4% compounding semiannually. What is the present value of the investment if Jessa’s children leave for college in 11 years?

$8,623.98

$6,665.39

$8,856.83

$7.025.32

I keep getting this as my answer: 1669.7549618492145787
which is nowhere close to any of the answer choices given above. ):

Answer 1

This is how I have my problem set up

FV = 525(1 + (5.4/100))^(2 * 11)

Answer 2

@ganeshie8 Mind helping me again? lol :p

Answer 3

Would I set it like this?

FV = 525/(1 + (5.4/2))^(2 * 11)

Answer 4

Never mind..that didn't work either :l

Answer 5

hint : its not a single deposit

Answer 6

well you need the formula for the future value of an annuity....

an annuity is a situation where the same amount is deposited under the same conditions....

the formula is

\[FV = M \times \frac{(1 + r)^n -1}{r}\]


M is the regular contribution... all the other information is the same as compound interest

Answer 7

every 6 months she is depositing,
that means without considering interest itself, she should get : 525*2*11 money,

your 1669 is very less

Answer 8

^^

Answer 9

So,

M = 525
r = 5.4
n = 2

Right?

Answer 10

oops I gave future value when you want the present value...

so you need to take the future value answer... and divide it by (1 +r)^n

to find out how much you would need to invest now to get the same amount in 11 years

Answer 11

the present value formula is

\[PV = M \times \frac{(1 + r)^n -1}{r(1 + r)^n}\]

Answer 12

so if you calculate the future value of the annuity it will be $30902.90


so what amount do you need to invest now... for the same return

uses the compound interest fromula

\[30902.90 = P( 1 + 0.054)^{22}\]

just make P the subject

Answer 13

well its a bit to much.... that will depend on then the $525 deposits are made.... at the beginning or end of each period....

Answer 14

when we're not explicitly told, we can assume its an ordinary annuity

Answer 15

I am so lost...

Answer 16

I tried both of your formulas and I still get the wrong answers

Answer 17

...

Answer 18

I'll just guess. Thanks anyways.

Answer 19

its the last answer

Answer 20

No its not

Answer 21

well there you go... I just worked it out on a spread sheet and got the last answer...

Answer 22

This tells me otherwise though
http://www.wolframalpha.com/input/?i=525*%28%281+%2B+0.054%2F2%29%5E%282+*+11%29-1%29%2F%280.054%2F2%29++%3D+x%281+%2B+0.054%2F2%29%5E%282*11%29

Answer 23

ok... there in lies the problem.... the interest rate was 5.4% per annum and not 5.4% per half year....

now it makes more sense....

Answer 24

So, the link I sent you was correct?

Answer 25

which is $8623.98

Answer 26

I'll take that as a yes lol

Answer 27

so find the future value using the formula

\[FV = 525 \times \frac{(1 + 0.027)^{22} -1}{0.027}\]

which is

$15497.40

so now use the compound interest formula with the futrue value \[15497.4 = P \times (1 + 0.027)^{22}\]

solve for P and you get answer A

Answer 28

Just checked and it was correct. (: Thanks

Answer 29

amazing how omitting p.a. changes the question

Answer 30

Indeed lol