Calculating Annuity

• Oct 13th 2010, 11:03 AM
focustnr29
Calculating Annuity
I need some help with a math problem that I was assigned that I have been working on for a while now and just cant figure it out. Any help would be appreciated. here is the problem...

1. Jack, a beginning freshman, wants to buy a used truck when he gets his associates degree. He believes it will cost \$3000 for the make and model he wants. He wants to start an annuity savings account for this purpose. Today is September 1, 2013 and jack wants to buy the truck June 1, 2015. His funds will be deposited into an account paying 2.75% APR compounded weekly.
a. How much money must jack deposit at the end of each week so as to end up with \$3000 on 6/1/15?

b. what is the present value of this annuity?

c. if on june 1, 2015, jack decided not to buy the truck but rather to keep the money in the account earning compound interest(same interest rate, no further deposits) how much money would be in the account on october 1, 2015?

Thanks to everyone in advance for all the help... this one is killing me.
• Oct 13th 2010, 10:53 PM
CaptainBlack
Quote:

Originally Posted by focustnr29
I need some help with a math problem that I was assigned that I have been working on for a while now and just cant figure it out. Any help would be appreciated. here is the problem...

1. Jack, a beginning freshman, wants to buy a used truck when he gets his associates degree. He believes it will cost \$3000 for the make and model he wants. He wants to start an annuity savings account for this purpose. Today is September 1, 2013 and jack wants to buy the truck June 1, 2015. His funds will be deposited into an account paying 2.75% APR compounded weekly.
a. How much money must jack deposit at the end of each week so as to end up with \$3000 on 6/1/15?

b. what is the present value of this annuity?

c. if on june 1, 2015, jack decided not to buy the truck but rather to keep the money in the account earning compound interest(same interest rate, no further deposits) how much money would be in the account on october 1, 2015?

Thanks to everyone in advance for all the help... this one is killing me.

You need to know the number of periods involved, these are weeks and you will have to count how many there are between the start and end dates yourself.

The weekly interest rate is $2.75/(365.25/7)\approx 0.0527 \%$, and let $m=1+(0.0527/100)=1.000527$

Then the amound available after $n$ periods is:

$A_n=d \dfrac{m}{m-1}[m^n-1]$

where $d$ is the amount deposited each period.

So for part a you need to solve for $n$ in:

$d \dfrac{m}{m-1}[m^n-1]=3000$

You will have to do this numerically.

CB
• Oct 14th 2010, 12:43 AM
Wilmer
Quote:

Originally Posted by focustnr29
Jack, a beginning freshman, wants to buy a used truck when he gets his associates degree. He believes it will cost \$3000 for the make and model he wants. He wants to start an annuity savings account for this purpose. Today is September 1, 2013 and jack wants to buy the truck June 1, 2015. His funds will be deposited into an account paying 2.75% APR compounded weekly.
How much money must jack deposit at the end of each week so as to end up with \$3000 on 6/1/15?

I'm looking at this as a savings account in which a weekly deposit of \$w will be
made starting ~Sep 8/13 and ending ~Jun 1/15 at rate of .0275/52 weekly;
and also assuming this represents exactly 91 weeks.

Formula: w = fi / [(1 + i)^n - 1] :
f = future value, i = periodic rate, n = number of periods

w = 3000(.0275 / 52) / [(1 + .0275/52)^91 - 1] = 32.18884... ; so 32.19
• Oct 14th 2010, 12:06 PM
focustnr29
Thank you to you both this really helps
• Oct 17th 2010, 11:35 PM
thekiterunner
I posted this web link in a topic above but just in case u didnt see it this website i found also explains annuities which you may find handy.

http://www.weallstartsomewhere.com/finmaths.php