# Sinking Fund Problem

• Apr 26th 2008, 09:10 PM
bobhanks
Sinking Fund Problem
Hello, my name is Bob Hanks, and I am working on my second bachelor's degree in aviation management. I have an URGENT sinking fund problem that will probably be easy to solve for most of the Forum members, but I have not worked with sinking funds in the past.

Here is the problem, in the context of an airport financing its activities:

A sinking fund that earns 10% was established to retire bonds with a total face amount of \$2 million in 10 years. How much must the equal end of year payments into the fund be?

I would be grateful for your speedy assistance.

Thanks,

Bob Hanks

April 26, 2008
• Apr 26th 2008, 09:58 PM
Aryth
The formula for a Sinking Fund is as follows-

The periodic payment R required to accumulate a sum of S dollars over n periods with interest charged at the rate of i per period is:

$R = \frac{iS}{(1+i)^n - 1}$

We know that:

$S = 2,000,000$

$i = 10\% = .1$

$n = 10$

All you have to do, is solve this equation:

$R = \frac{0.1*2,000,000}{(1+0.1)^{10} - 1}$
• Apr 27th 2008, 10:38 AM
bobhanks
Sinking fund factor?
Thanks ever so much. Therefore there is no sinking fund factor (sff) taken from a table that must be used to calculate the amount that must be paid into the fund annually?

Also, in the equation you kindly provided is that portion of the equation to be raised to the power of 10?

(By the way, for my insanity, what is the answer...I promise never to bug anyone again)

Thanks,

Bob Hanks
• Apr 27th 2008, 10:16 PM
Aryth
The uniform series sinking fund factor is:

$USSF = \frac{i}{(1+i)^n - 1}$

As you can tell, the equation I provided is simply the USSF multiplied by the total amount, thus, over longer periods of time, the amount of money you have to pay per year decreases.

And yes, it is to the power of ten.

$R = \ 125490.79$