Present value Annuity

thekiterunner · #1 $Old$ November 5th, 2009, 03:33 AM

1. A mobile phone contract consists of a $115 payment at the beginning of each month over two years with the first three months free. What is the value at the end of two years if the rate of interest is 9% p.a.?

2. What is the effective interest rate?

I was hoping that someone could help me work this out becuase i have no idea where to even begin.

Wilmer · #2 $Old$ November 5th, 2009, 06:55 AM

Quote:

Originally Posted by thekiterunner $View Post$

1. A mobile phone contract consists of a $115 payment at the beginning of each month over two years with the first three months free. What is the value at the end of two years if the rate of interest is 9% p.a.?

2. What is the effective interest rate?

I was hoping that someone could help me work this out becuase i have no idea where to even begin.

Please clarify: you're first talking of present value, then end up with a
question asking for the future value of the equivalent of $115 deposited
monthly for 21 months, on 1st day of each month...

If you don't know enough to clarify it, then ask whoever gave you the
problem to clarify it.

As it stands, the cash flows are:
jan 1/01 : 0
feb 1/01 : 0
mar 1/01 : 0
apr 1/01 : 115
may 1/01: 115
...
nov 1/02 : 115
dec 1/02 : 115
dec 31/02 : ? : your question asks for a value at this point ?

Also, can you tell us why you have no idea; bad teacher? Missed classes?

thekiterunner · #3 $Old$ November 5th, 2009, 07:07 PM

thank you...that provided me with no information whatsoever...no i didn't skip class and my teacher is great...its just a really difficult question...which clearly not even you could do...

TKHunny · #4 $Old$ November 5th, 2009, 08:16 PM

What have you TRIED? What is your plan? Since you have been to class, did you pay attention?

What do you know of "Basic Principles"? You should be able to solve virtually anything from Basic Principles.

"Over 2 years" - 24 payments

"first 3 free" - 21 payments

Annual Interest: i = 0.09

Monthly Interest: i12 = 0.09/12 = 0.0075

Monthly Accumluation: r = 1 + i12 = 1.0075

These are all the tools you need.

Last Payment is worth 115*r
Second to last payment is worth 115*r^2
Third to last payment is worth 115*r^3

...are we seeing a pattern?

Now one must simply add up the 21 values. Let's see what you get.

Wilmer · #5 $Old$ November 5th, 2009, 08:35 PM

ONCE MORE:

The problem is titled : Present value Annuity

The question is worded:
What is the value at the end of two years if the rate of interest is 9% p.a.?
(which means FUTURE value)

But if for some reason that's considered normal, then value end of 2 years
= 115(1 + .09/12)[(1 + .09/12)^21 - 1)] / (.09/12) = 2624.56

And in case it's decided that the question should be: "what is the present value?":
2624.56 / (1 + .09/12)^24 = 2193.69

mukrosa · #6 $Old$ November 7th, 2009, 01:26 AM

hey this is a deferred annuity and wilmer has used its formula hope you understood it