series help (1 Viewer)

[gg1994]

can someone explain how to do this (working etc and why your doing it), im getting every question right but not this one and i dont know what im doing wrong.
thanks
Jane puts $300 into an account
at the beginning of each year. If 6%
p.a. interest is paid quarterly, how much
money will Jane have at the
end of the 5 years?

 

[zeebobDD]

use the same basic stuff you've used for other questions, just change the 6% from a quarterly rate

 

[gg1994]

use the same basic stuff you've used for other questions, just change the 6% from a quarterly rate

yeah thats what i'm doing but according to the answers its wrong. if you do it what do you get? you dont have to do it if you dont want lol

 

[zeebobDD]

yeah thats what i'm doing but according to the answers its wrong. if you do it what do you get? you dont have to do it if you dont want lol

what is the answer at the back of the book? and you should post what you've done so people can spot your mistake and tell you where you went wrong

 

[gg1994]

the answers $1799.79
and im doing this 0.06/4 + 1 = 1.015
and then 300 [1.015(1.015^20 - 1) / 1.015 - 1] and i get like 7000 or something like that
am i getting my formulas mixed up or do you do something different with annuity? is this even annuity? did i read the question wrong. any help would be awesome cause ive completely confused myself by now. thanks

 

[zeebobDD]

yeah you've got the right interest, though i think this is just simple compound interest, or you could do it this method ; http://www.1728.org/annuity2.htm

but the answer im getting is like 1568 in the first year she will get 300 x (1.015) then the second year it will be 300 x (1.015)^2 therefore in that 2 year period you add both the amounts together to see her total, same case for the 5 years

 

[zeebobDD]

there are 3 QUARTERS In a year not 4 LOL huge fail

 

[Timske]

​<a href="http://www.codecogs.com/eqnedit.php?latex=\\A_{1}=300(1.015)^{20}\\A_{2}=300(1.015)^{16}\\A_{3}=300(1.015)^{12}\\A_{4}=300(1.015)^{8}\\A_{5}=300(1.015)^{4}\\\ Total= A_{1}@plus;A_{2}@plus;A_{3}@plus;A_{4}@plus;A_{5}\\\ Total = 300(1.015)^{20}@plus;300(1.015)^{16}@plus;300(1.015)^{12}@plus;300(1.015)^{8}@plus;300(1.015)^{4}\\ Total=300\left [ (1.015)^{4}@plus;(1.015)^{8}@plus;(1.015)^{12}@plus;(1.015)^{16}@plus;(1.015)^{20} \right ] \\\ \therefore a=1.015^4 ~~ r=1.015^4 ~~n=20 \\\\ Total=300\left [ \frac{1.015^4(1.015^{20}-1)}{(1.015^4-1)} \right ] = \$ 1799.79" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\\A_{1}=300(1.015)^{20}\\A_{2}=300(1.015)^{16}\\A_{3}=300(1.015)^{12}\\A_{4}=300(1.015)^{8}\\A_{5}=300(1.015)^{4}\\\ Total= A_{1}+A_{2}+A_{3}+A_{4}+A_{5}\\\ Total = 300(1.015)^{20}+300(1.015)^{16}+300(1.015)^{12}+300(1.015)^{8}+300(1.015)^{4}\\ Total=300\left [ (1.015)^{4}+(1.015)^{8}+(1.015)^{12}+(1.015)^{16}+(1.015)^{20} \right ] \\\ \therefore a=1.015^4 ~~ r=1.015^4 ~~n=20 \\\\ Total=300\left [ \frac{1.015^4(1.015^{20}-1)}{(1.015^4-1)} \right ] = \$ 1799.79" title="\\A_{1}=300(1.015)^{20}\\A_{2}=300(1.015)^{16}\\A_{3}=300(1.015)^{12}\\A_{4}=300(1.015)^{8}\\A_{5}=300(1.015)^{4}\\\ Total= A_{1}+A_{2}+A_{3}+A_{4}+A_{5}\\\ Total = 300(1.015)^{20}+300(1.015)^{16}+300(1.015)^{12}+300(1.015)^{8}+300(1.015)^{4}\\ Total=300\left [ (1.015)^{4}+(1.015)^{8}+(1.015)^{12}+(1.015)^{16}+(1.015)^{20} \right ] \\\ \therefore a=1.015^4 ~~ r=1.015^4 ~~n=20 \\\\ Total=300\left [ \frac{1.015^4(1.015^{20}-1)}{(1.015^4-1)} \right ] = \$ 1799.79" /></a>

nvm made a mistake

 

[Jared_Stanfield]

yeah you've got the right interest, though i think this is just simple compound interest, or you could do it this method ; http://www.1728.org/annuity2.htm

but the answer im getting is like 1568 in the first year she will get 300 x (1.015) then the second year it will be 300 x (1.015)^2 therefore in that 2 year period you add both the amounts together to see her total, same case for the 5 years

Newbs aren't allowed to use annuity formulas.

There are also a number of little tricks that stop you from using annuity formulas (or at least the one given on that website).

i) The annuity formula given there is when the payments are at the end of the period (called an ordinary annuity) whereas this problem involves cash flows at the start( called a deferred annuity).

ii) The compounding period does not match the cash flow frequency. You need to compute an "effective" interest rate, an equivalent rate that compounds yearly.


The normal formula for the future value of an annuity is (C/r) ( (1+r)^n -1)

However, since this is a deferred annuity we need to take the future value of the above by one year (multiply it by (1+r))

V= (C/r) (1+r) [ (1+r)^n -1 ]

Now we just need to r.

The effective annual interest rate is [ 1 + (0.06 / 4) ] ^ 4 -1 = 0.0613636

C=$300 , r= 0.0613636 , n= 5periods

V= (300 / 0.0613636) (1.0613636) [ (1.0613636)^5 -1 ] = 1799.79472 = $1799.79


But that is only for university finance students. You have to derive all the stuff.