Question

. Mia will need to have $25,000 six years from today. What she will have to put back in the bank today so she will have $25,000 six years hence. Her bank pays 5 percent compounded semiannually. What is the amount Mia will have to deposit is?

Answer 1

$25,000(1+.05/2)^12=33,622.22 ?

Answer 2

You're on the right track. But that's working out what 25,000 invested now would be become. The formula for compound interest, as you know, is\[\Large {A_t} = {A_0}{\left( {1 + \frac{r}{n}} \right)^{nt}}\]So simply rearrange to make \({A_0}\) the subject:\[\Large {A_0} = \frac{{{A_t}}}{{{{\left( {1 + \frac{r}{n}} \right)}^{nt}}}}\]

Answer 3

so, 25,000= 33,622.2291+.05/2)^12 ?

Answer 4

No no no. \({A_0}\) is what you need to invest now to achieve 25,000 in 6 years (at 5% interest rate compounded semi-annually), which is what the question is asking, correct?

Answer 5

oh. im really bad at math so im sorry... lol. so, i would take:
25000/(1+.05/2)^12= 18,588.89 or 18,588.90 ?

Answer 6

Yes! =)

Answer 7

sweet. thank you.

Answer 8

No worries.