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anonymous
 one year ago
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.
anonymous
 one year ago
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.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Need help with the recursive equation and how to think, im all out of ideas here.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.01123.6 is what im guessing, dont quote me lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0don't give out an answer. 0_o

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and im pretty sure its wrong

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the annuity is 20$ and the intrest is compounded monthly for 4 years

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the first thing you would do is get the intrest plus the principle

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and then add 20 for 4 years

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you could use this website here to find out the interest + principal http://www.calculatorsoup.com/calculators/financial/

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Im not interested in calculators, I want to make that into a recursive equation and then solve the recurisve equation

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Y_{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
 one year ago
Best ResponseYou've already chosen the best response.0well 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
 one year ago
Best ResponseYou've already chosen the best response.0@IrishBoy123 do you anything about recursive equations?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1what you've built seems right http://www.math.kth.se/math/GRU/2012.2013/SF1610/CINTE/mastertheorem.pdf resolving, 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
 one year ago
Best ResponseYou've already chosen the best response.1Example 2.2 looks a bit like yours

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[Y _{n+1}1,06Y _{n}200=0\] is our homogenous equation and to solve that you make a characteristic equation: \[r1.06=0\] 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 \[A1.06A=0\] \[A(11.06)=0\] \[0.06A=200\] \[A=\frac{ 200 }{ 0.06 } = 3333.3\] So A must be equal to 3333.3 then we have to make the common solution \[y _{n}=(C _{1}*n+C _{2})*1.063333\] as we know \[y _{0}=100\] and \[y _{1}=126\] so try that with the common solution \[y _{0}=(C_{1}*0 + C _{2})*1.06  333.3 = 100\] \[C _{2}=408.77\] \[y _{1}=(C _{1}*1+C _{2})*1.06333.3=126\] \[C _{1}=\frac{ 1.06C _{2}+459.3 }{ 1.06}\] \[C _{1}=\frac{ 1.06*408.77+459.3 }{ 1.06}\ \[C _{1}=24.53 the solution we were looking for is \[Y _{n}=(24.53*n+408.77)*1.06333\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and the solution we are looking for is \[Y _{n}=(24.52*n+408.77)*1.06333\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and I ment that A must be equal to 333.3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@IrishBoy123 check this out now

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1seems *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

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1ouch, might be annual 6% so 6/12 monthly.....

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1this is what i mean by exponents.... https://gyazo.com/8e485926c771572c6f243e742837f94d

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oops forgot the exponent over r in the formula!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0he should have 6786.36 dollars after 4 years?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1no, 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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