anonymous
  • anonymous
The first day of a new year Adam opens a bank account and deposit 100 dollars . Then he deposits 20 dollars every moth with the interest rate, 6 % that is calculated monthly. How much money does Adam have on his account exactly 4 years after he opened the account ? Set up a proper recursive equation and solve this.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Need help with the recursive equation and how to think, im all out of ideas here.
anonymous
  • anonymous
1123.6 is what im guessing, dont quote me lol
anonymous
  • anonymous
what?

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anonymous
  • anonymous
don't give out an answer. 0_o
anonymous
  • anonymous
and im pretty sure its wrong
anonymous
  • anonymous
so the annuity is 20$ and the intrest is compounded monthly for 4 years
anonymous
  • anonymous
the first thing you would do is get the intrest plus the principle
anonymous
  • anonymous
and then add 20 for 4 years
anonymous
  • anonymous
you could use this website here to find out the interest + principal http://www.calculatorsoup.com/calculators/financial/
anonymous
  • anonymous
Im not interested in calculators, I want to make that into a recursive equation and then solve the recurisve equation
anonymous
  • anonymous
Y_{0}=100$ Y_{1}=100*1.06+20=126$ Y_{2}=126*1.06+20=153.56$ Y_{0}=100$ Y_{1}=Y_{0}*1.06+200 Y_{2}=Y_{1}*1.06+200 that is the recursive sequence so then you have \[Y _{n+1} = 1.06Y _{n}+200\] and then solve that one....
anonymous
  • anonymous
well i don't know much there because my finance teacher always let us use calculators but there are the equations there in calculator soup. That's all i can help you with then sorry.
anonymous
  • anonymous
@IrishBoy123 do you anything about recursive equations?
IrishBoy123
  • IrishBoy123
what you've built seems right http://www.math.kth.se/math/GRU/2012.2013/SF1610/CINTE/mastertheorem.pdf re-solving, some techniques here, but nothing that I am au fait with, would need to read it myself :-) happy to try help if you are in need
IrishBoy123
  • IrishBoy123
Example 2.2 looks a bit like yours
anonymous
  • anonymous
\[Y _{n+1}-1,06Y _{n}-200=0\] is our homogenous equation and to solve that you make a characteristic equation: \[r-1.06=0\] which means that our root must be r=1.06 and then we guess a particular equation of the form A and if we put that in the equation it will be \[A-1.06A=0\] \[A(1-1.06)=0\] \[0.06A=200\] \[A=\frac{ 200 }{ 0.06 } = 3333.3\] So A must be equal to 3333.3 then we have to make the common solution \[y _{n}=(C _{1}*n+C _{2})*1.06-3333\] as we know \[y _{0}=100\] and \[y _{1}=126\] so try that with the common solution \[y _{0}=(C_{1}*0 + C _{2})*1.06 - 333.3 = 100\] \[C _{2}=408.77\] \[y _{1}=(C _{1}*1+C _{2})*1.06-333.3=126\] \[C _{1}=\frac{ -1.06C _{2}+459.3 }{ 1.06}\] \[C _{1}=\frac{ -1.06*408.77+459.3 }{ 1.06}\ \[C _{1}=24.53 the solution we were looking for is \[Y _{n}=(24.53*n+408.77)*1.06-333\]
anonymous
  • anonymous
\[C _{1}=24.53\]
anonymous
  • anonymous
and the solution we are looking for is \[Y _{n}=(24.52*n+408.77)*1.06-333\]
anonymous
  • anonymous
and I ment that A must be equal to 333.3
anonymous
  • anonymous
@IrishBoy123 check this out now
IrishBoy123
  • IrishBoy123
seems *slightly* out. and i would expect to see a \(1.06^n\) in there for sure to get the compounding have put them in a spreasdheet - attached for checking pruposes
1 Attachment
IrishBoy123
  • IrishBoy123
ouch, might be annual 6% so 6/12 monthly.....
1 Attachment
IrishBoy123
  • IrishBoy123
this is what i mean by exponents.... https://gyazo.com/8e485926c771572c6f243e742837f94d
anonymous
  • anonymous
oops forgot the exponent over r in the formula!
anonymous
  • anonymous
he should have 6786.36 dollars after 4 years?
anonymous
  • anonymous
@IrishBoy123
IrishBoy123
  • IrishBoy123
no, my bad look at the second pdf of same name. i think the 6% is annual so you apply 1/12 [not strictly true] of that per month strictly speaking you break 6% pa into monthly by saying \[ (1+r_m)^{12} = 1 +0.06\] \[ (1+0.06)^{\frac{1}{12}} - 1 = r_m\] gives 0.4867551% monthly interest, whereas \[\frac{6\%}{12} = 0.5\%\] that will make a difference to how you do this

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