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Sinking fund

Jack borrowed $25000 at 8% for 5 years. He also opened a sinking fund account that pays 6%. How much should he pay for the interest on his loan? What size deposit should he make to his sinking fund to pay off the principal of his loan on time?

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Thomas L. | Mathematics TutorMathematics Tutor
4.9 4.9 (26 lesson ratings) (26)
Sinking funds bleh!  Since it has not been state I'm going to assume annual payments instead of teh standard monthly.  So how a sinking fund works is a person borrows money but instead of making the regular payments on it, they only pay interest each year.  In this problem 8% of $25000 is  $2000.  That means at the end of every year, he will pay the bank $2000 in interest and nothing towards the $25,000. 
But Jack isn't going to wait till year 5 to just have $25,000 to pay back.  He is going to go to a different bank and make deposits that will give him 6% interest. 
So at this other bank he needs to accumulate $25,000 in 5 years at a 6% interest rate.  If you have the formula for sn that will be helpful.  It is basically 25,000 = X(1.065 - 1)/(.06), where X is the annual payment to Bank 2.  When I compute I get 4434.91.
The question doesn't ask for it but sometimes it will ask for the total annual payment which would be $2000 + 4434.91 = 6434.91