Question

An engineer has a fluctuating future budget for the maintenance of a particular machine. During each of the first 5 years, $10,000 per year will be geted. During the second 5 years, the annual budget will be $15,000 per year. In addition, $5000 will be budgeted for an overhaul of the machine at the | end of the fourth year, and again at the end of the eighth year. What uniform annual expenditure would be equivalent, if interest is 8% per year?

Answer 1

The question wants us to find an amount of expenditure(say x) which shall be equal in all years, so that the annual budget shall remain the same as it was previously considered. In other words, we need to find the present value (PV) of the annual expenditure as stated in the question and equate it with the present value of x over the period of 10 years. The rate of interest is given in the question as 8%. The below attached handwritten solution will provide a better picture for understanding. Hope it helps.

Solution to question : - Rough_cigom for understanding 5 6 7 8 9 10 Years Ludgeted Additional I 2 3 4 10,000_10.000 1010 10,000 500D 19000 ISUUD USD 1500 15000 15000 _5000 Tual (DK DK DK SKOK ISK ISK 20K SK ISK Ik stands for too - Present Value (N) the above budgeted expenses + ISDOD +10000 15,000 10000 I.DE + 10,000+ 10,000 LOPE Isto 1.097 Log 3 1.084 in 1.084 70,000 + 75,000 + 15,00 4.09 1.089 1.00 = $87014 (Approx) Now we need on amount which we wel bucket every year -- so that is uniform, but still the present value of n for 10 years will be equivalent to $87084 (Appose). Hently on the Annudised factor (AF) for $1. for 10 years is - 671 than prese On a calculator, phebe 1: 1.0% 10 times, then press GT] Thence, the equivalent amount anual expenditure shall be 387064__ 412975___ 6.71 Hence it we innest $12,975 per yeah, then the PN q it shall I be equal to PV & the annual expenditure as given in question Llie. $87064)