mariomintchev
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mariomintchev
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mariomintchev
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annuity formula: A=R*( (1+i)^n - 1 ) / (i)
mariomintchev
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compound formula: A=P(1+ r/n)^nt
glamsunnyskylar
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Sorry, it won't load for me, or else I really would help you.
mariomintchev
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A company contributes $150 per month into a retirement fund paying a nominal interest rate of 4.40% APR compounded monthly and employees are permitted to invest up to $ 2,900 per year into another retirement fund which pays a nominal interest rate of 4.40% APR compounded annually.
How large can the combined retirement fund be worth in 25 years?
anonymous
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we can do this if you have the formulas
mariomintchev
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i do but im not getting the results.
anonymous
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i guess this is the formula you wrote
A=R*( (1+i)^n - 1 ) / (i)
but i am not sure what all the variable represent
mariomintchev
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ok A stands for Annuity, R is the payment, i is the APR/frequency of pay, and n is the frequency of pay
mariomintchev
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so for example "i" would be .044/12
anonymous
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ok
anonymous
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then \[\frac{150(1+\frac{.044}{12})^{12-1}}{\frac{.044}{12}}\] but that can't be right, because there is no time mentioned in the formula
is perhaps \(n\) the number of payments?
anonymous
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that would make more sense
it can't really be the frequency of the payments minus one
there has to be something mentioning the number of payments made
mariomintchev
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n is 12 *25 i think
anonymous
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ooh ok it is the number of payments
anonymous
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\[\frac{150(1+\frac{.044}{12})^{12\times 25-1}}{\frac{.044}{12}}\]
mariomintchev
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why minus 1?
anonymous
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that is what you wrote
anonymous
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you wrote \(n-1\) i assumed that was in the exponent
anonymous
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makes sense if you are summing a geometric sequence i think
mariomintchev
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its not n-1. its raised to n and then you subtract everything in the parenthesis by 1.
anonymous
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oh damn ok
mariomintchev
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A = R ( ( 1+i)^(n) - 1 ) / (i)
anonymous
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\[\frac{150((1+\frac{.044}{12})^{300}-1)}{\frac{.044}{12}}\]
mariomintchev
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yeah thats what i got earlier too
mariomintchev
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what do we do with the 2900?
anonymous
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redo it
anonymous
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\[2900((1.044)^{25}-1)\]
anonymous
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since it is yearly, \(i=1\)
mariomintchev
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why dont we divide or multiply by 12 anywhere?
anonymous
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not if it is yearly, no
that is for monthly
mariomintchev
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o i think thats probably what ive been doing wrong
anonymous
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2900 per year compounded annually it says
mariomintchev
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THANKS! :)