# Sinking Fund Problem

A sinking fund that earns 10% was established to retire bonds with a total face amount of $2 million in 10 years. How much must the equal end of year payments into the fund be? I would be grateful for your speedy assistance. Thanks, Bob Hanks My E-mail address is bobhanks@verizon.net April 26, 2008 • Apr 26th 2008, 09:58 PM Aryth The formula for a Sinking Fund is as follows- The periodic payment R required to accumulate a sum of S dollars over n periods with interest charged at the rate of i per period is:$\displaystyle R = \frac{iS}{(1+i)^n - 1}$We know that:$\displaystyle S = 2,000,000\displaystyle i = 10\% = .1\displaystyle n = 10$All you have to do, is solve this equation:$\displaystyle R = \frac{0.1*2,000,000}{(1+0.1)^{10} - 1}$• Apr 27th 2008, 10:38 AM bobhanks Sinking fund factor? Thanks ever so much. Therefore there is no sinking fund factor (sff) taken from a table that must be used to calculate the amount that must be paid into the fund annually? Also, in the equation you kindly provided is that portion of the equation to be raised to the power of 10? (By the way, for my insanity, what is the answer...I promise never to bug anyone again) Thanks, Bob Hanks • Apr 27th 2008, 10:16 PM Aryth The uniform series sinking fund factor is:$\displaystyle USSF = \frac{i}{(1+i)^n - 1}$As you can tell, the equation I provided is simply the USSF multiplied by the total amount, thus, over longer periods of time, the amount of money you have to pay per year decreases. And yes, it is to the power of ten. The answer is:$\displaystyle R = \$125490.79$