You invest 10,000 at time 0. What is the value of the investment at time 4, if the annual effective interest rate is characterized by the formula i(sub t) = .007t^2?

Question

cwrw238 · Answer

i(sub t) - it probably means interest at time t
so its .007* 4^2

cwrw238 · Answer

times 10,000?

anonymous · Answer

nah, i have tried that.

cwrw238 · Answer

do you know the correct answer?

anonymous · Answer

my answer choices are 10,238.56,  10,876.36,  11,673.40,  and 12,236.60

anonymous · Answer

i feel like i have tried all of the formulas i was given

cwrw238 · Answer

right  .007*16* 10000 =  1120

those answers are the accumulated total of course

anonymous · Answer

but 1120 isnt an answer i can choose from...

cwrw238 · Answer

i know - try 0.007*1^2 *10000 + 0.007*2^2 *10000 + 0.007*3^2 *10000 + 1120
 i e total interest over 4 years and add this to 10,000

cwrw238 · Answer

no that gives 12,030
-  aah - it could be compounded

anonymous · Answer

sorry, distracted. homework is taking so long my baby woke up from her nap...

anonymous · Answer

yes, tried that too...

phi · Answer

they are applying 0.007t^2  each year, compounded each year
use 0.007  for the interest rate the first year
0.007*4 then 2nd year, 
etc

anonymous · Answer

shouldn't there be a formula for that?

phi · Answer

maybe, but I don't know it.  Computers can do these things without a closed form, just do the calculation year by year...

cwrw238 · Answer

yea - i tried that but got 12,156.02  - maybe i made a mistake somewhere

phi · Answer

try again...

phi · Answer

did you compound it?

cwrw238 · Answer

yes as you said * 007 times  .007*4 then 0.007*8 then ).007*16
on the compounded amount

cwrw238 · Answer

-same answer second time - could try third i suppose....

phi · Answer

P*(1+0.007)*(1+0.007*4)(1+0.007*9)(1+0.007*16)

cwrw238 · Answer

yes - though isn't it 1 + 0.007*8?

phi · Answer

t^2  for t=3

cwrw238 · Answer

ahhhhh - my mistake

phi · Answer

you must be thinking 2^t

cwrw238 · Answer

thats it 12,236.60

cwrw238 · Answer

yes - i was

anonymous · Answer

awesome!  i was reading along and learning.  ..hard to do with a one-year old running around

anonymous · Answer

thank you guys a lot!

cwrw238 · Answer

yw

cwrw238 · Answer

i think i'll take a break too - i'm making a few too many mistakes today

anonymous · Answer

@cwrw238 haha!  not as many as me!  and give yourself that break....with a kit kat bar! bam! been waiting to use that

cwrw238 · Answer

lol
ok