## mariomintchev 2 years ago I really need help solving this...

1. mariomintchev

2. mariomintchev

annuity formula: A=R*( (1+i)^n - 1 ) / (i)

3. mariomintchev

compound formula: A=P(1+ r/n)^nt

4. glamsunnyskylar

5. mariomintchev

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?

6. satellite73

we can do this if you have the formulas

7. mariomintchev

i do but im not getting the results.

8. satellite73

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

9. mariomintchev

ok A stands for Annuity, R is the payment, i is the APR/frequency of pay, and n is the frequency of pay

10. mariomintchev

so for example "i" would be .044/12

11. satellite73

ok

12. satellite73

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?

13. satellite73

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

14. mariomintchev

n is 12 *25 i think

15. satellite73

ooh ok it is the number of payments

16. satellite73

$\frac{150(1+\frac{.044}{12})^{12\times 25-1}}{\frac{.044}{12}}$

17. mariomintchev

why minus 1?

18. satellite73

that is what you wrote

19. satellite73

you wrote $$n-1$$ i assumed that was in the exponent

20. satellite73

makes sense if you are summing a geometric sequence i think

21. mariomintchev

its not n-1. its raised to n and then you subtract everything in the parenthesis by 1.

22. satellite73

oh damn ok

23. mariomintchev

A = R ( ( 1+i)^(n) - 1 ) / (i)

24. satellite73

$\frac{150((1+\frac{.044}{12})^{300}-1)}{\frac{.044}{12}}$

25. satellite73

i get 81741.62 rounded http://www.wolframalpha.com/input/?i= \frac{150%28%281%2B\frac{.044}{12}%29^{300}-1%29}{\frac{.044}{12}}

26. mariomintchev

yeah thats what i got earlier too

27. mariomintchev

what do we do with the 2900?

28. satellite73

redo it

29. satellite73

$2900((1.044)^{25}-1)$

30. satellite73

since it is yearly, $$i=1$$

31. mariomintchev

why dont we divide or multiply by 12 anywhere?

32. satellite73

not if it is yearly, no that is for monthly

33. mariomintchev

o i think thats probably what ive been doing wrong

34. satellite73

2900 per year compounded annually it says

35. mariomintchev

THANKS! :)