Series and Sequences (1 Viewer)

[star*eyed]

Please Help With This Maths Question

How would i do this question?

toms father paid $500 into an account when tom was born. he pays $500 into it every year on toms bday until tom is 18. if the account accrued interest at 8% per ANNUM compunded MONTHLY, how much will tom revieve on his bday.

The bit that is confusing me is the fact that the 500 is only put in annually, but the interest is payed monthley.

ANY help is greatly appreciated.

oh and if it helps the answer according to the book is $ 20880.97

 

[Shady01]

work out how much he puts in monthly so 500/12 then u can apply yr forumla for monhtly interest 18x24 etc etc. I hope

btw what text book is this out of i think ive done it before????

 

[star*eyed]

ummm extention 1 understanding yr 12 maths, THANX FOR UR HELP

 

[star*eyed]

ummm i just did it the way u said, and i get a different answer. i get $20136.95 when the answer is $ 20880.97. WHAT AM I DOING WRONG!!!!!!!!!

 

[abcd9146]

do it like this:
first $500 is paid interest 12 times so:
500 * (whateva is in one month)¹²
next $500 put is is another 12 months
and again...

and then you get a thing that is meant to look like
500*[(interest)¹²+(interest)²⁴+(interest)³⁶+..+(interest)⁹⁶]

try that, and see if you get the right answer... but its been so long that i forgot how to do these, so i basically just made up whatever above...

 

[star*eyed]

cept how do i make that into a GP or AP ???

 

[rama_v]

Here's how I would do it:

8% per annum = (8/12)% per month. To make it a yearly rate, we make R = (8/12)%¹². Therfore we get the R +1 = 1.0830... (store this number in your calculator).

Let A_n denote the amount of money in the bank at the end of n years.

A₁ = 500(1.0830..)
A₂ = 500(1.0830...)² + 500(1.0830...)
.
.
A_n = 500(1.0830...)ⁿ + 500(1.0830...)^n-1 +...+500(1.0830...)

= 500(1.0830...ⁿ + 1.0830...^n-1 +...+1.0830...]

Now in the brackets we have a gemetric sequence with a = 1.0830... and r = 1.0830..., with n = 18

A₁₈ = 500[(1.0830...)(1.0830...¹⁸ - 1) / (1.0830... - 1) ]

Once you put that mess in your calculator, you get
= $20880.97 which is the required answer.

 

[star*eyed]

hey thanx, but i put that into the calculator and i get the rate of 1??? i know its the right way to do it cause at one point i did get that 1.0830, cept then every other time it doesnt do it???? i put .08 /12, then i put the answer to the power of 12. when i add one i get 1. wats with that??

 

[rama_v]

hey thanx, but i put that into the calculator and i get the rate of 1??? i know its the right way to do it cause at one point i did get that 1.0830, cept then every other time it doesnt do it???? i put .08 /12, then i put the answer to the power of 12. when i add one i get 1. wats with that??

Punch in 8/12, divide by 100, add 1, then take the answer to the power of 12.

 

[star*eyed]

Thank You!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!