A person puts $5000 into a 20 year bond that pays interest annually at a rate of 5% and makes no other investments.

a) Describe a recursive sequence for , the money at the end of month .

b) Find a closed form for .

c) Use induction to prove your formula.

My struggle is figuring out how to write the recursive sequence in terms of months, not years, since the interest is only added at the end of the year (i.e. months 1 through 11 will be $5000 and then month 12 will be $5250).

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