Question

 

a township expects its population of 5,000 to grow annually at a rate of 5 percent. the township currently spends $300 per inhabitant but, as a result of inflation and wage increments, expects the per capital expenditure to grow annually by 7 percent. how much will the townships budget be after 10, 15, 20 years?

Answer 1

Calculation

	At Present	After 10 Years	After 15 Years	After 20 Years
Population (No.)	5000	=5000 * (1+5%)^10	=5000 * (1+5%)^15	=5000 * (1+5%)^20
Percapital Expenditure ($)	300	=300 * (1+7%)^10	=300 * (1+7%)^15	=300 * (1+7%)^20
Population grows at 5% per annum so used 5% for compounding and the respective period is used as exponential
Expenditure grows at 7% per annum so used 7% for compounding and the respective period is used as exponential
After Calculation
	At Present	After 10 Years	After 15 Years	After 20 Years
Population (No.)	5000	8,144	10,395	13,266
Percapital Expenditure ($)	300	590	828	1,161
Total Budget = Population * Percapital Expenditure
	At Present	After 10 Years	After 15 Years	After 20 Years
Total Budget	=5000*300	=8144*590	=10395*828	=13266*1161
`Total Budget in $	1,500,000	4,806,423	8,603,743	15,401,137