01:640:106 Lecture Notes - Lecture 12: Sinking Fund
2 Nov 2016
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Formula #6: pv = pmt an|i an|i = 1 - (1+i)^-n/i: a small company borrows ,000 from a group of investors at 5% interest compounded annually, due to be repaid in 2 years. Fv (of the loan) = ,000(1. 05)^2 = ,750. ,750 = pmt x s8t. 006875 = pmt(1. 006875^8-1/. 006875) = 8. 195169747. Pmt = ,459. 14 per quarter: john borrows from his uncle to buy a used car. Rather than deal with the hassle of monthly payments, they agree that he will repay the full amount at the end of 4 years. The interest rate will be 4. 5% compounded monthly. To make sure that he will have the full amount needed at the end of the 4 years, john sets up a sinking fund at a local bank and makes monthly payments to it. By pure coincidence, the local bank also pays 4. 5% interest. Fv = (1 + . 045/12)^48 = (1. 00375)^48 = . 07.
