Question

Every six months, Jacinda deposits $475 into an interest-bearing account to save for her children’s tuition. The interest rate on the account is 7.1% compounding semiannually. What is the present value of the investment if Jacinda’s children leave for college in 9 years?

Answer 1

@phi I know we worked out problems like this before but I cannot remember what I am supposed to do.

Answer 2

The wording may be somewhat tricky. Since payments of 475 are being deposited into the account, it's not really a "present value" problem. You have to use the future value formula, since the account is growing over time.

The formula itself is
\[FV=PMT\frac{(1+r/n)^n}{r/n}\]
and you're given
PMT = 475
r = 7.1% = 0.071
n = 2(18) = 36 (compounded semiannually, and 2 deposits per year for 9 years)

Answer 3

@SithsAndGiggles the answer choices are

$4,743.77
$5,080.58
$6,460.70
$6,239.21

when i did the formula i got 258549

Answer 4

Actually, I made a mistake when typing out the formula. It should be\[FV=PMT\frac{(1+r/n)^n-1}{r/n}\]
Unfortunately, solving for FV also gets an answer that's not one of the choices (I get $28,594.96). Give me a few minutes, I'll try to figure out what's wrong.

Answer 5

I'm quite certain this is the setup. Are you sure these choices correspond to this question?
http://www.wolframalpha.com/input/?i=475%28%28%281%2B.055%2F2%29%5E36%29-1%29%2F%28.055%2F2%29

It could also be a possibility that you left out some piece of information. Jacinda will definitely have $28,594.96 after 9 years of saving, assuming she starts saving up EXACTLY 9 years before the cash is needed. The only way the account would have a smaller balance is if we want to find out how much is in the account at a certain point after she started depositing, and THEN use the fact that there are 9 more years until the money will be needed.

Answer 6

How about using Present Value of an Ordinary Annuity ?
\[ PV= c \left( \frac{1}{i} - \frac{1}{i(1+i)^{nt}}\right) \]

with i = yearly interest/2 = 0.071/2 = 0.0355
1+i= 1.0355

c is the deposit (payment) = 475.00

Pv = 475*(1/0.0355 - 1/.0355 * (1.0355)^-18)=

if you copy and paste that into google, you get 6239.21

Answer 7

@phi, could you explain why present value is used as opposed to future value? I read that PV is typically used in problems involving debt and debt amortization, whereas FV is used for growth in an account.

Answer 8

I know these two formulas
\[ FV = pmt \frac{(1+i)^n -1}{i} \]
and
\[ FV =PV(1+i)^n \]

the second equation relates FV and PV
we could use these 2 to solve the problem, using
i=0.0355, n=18, and payment = 475