annuities questions (1 Viewer)

[hsc100]

Please can anyone help with these qestions?

1. At the start of 1997 a country town town in NSW had a population of 28000.It was estimated that this wuld increase each year by 9% of its population at the start of that year.What is the estimated population for the start of the year 2001?




2.Adriana is a student and saves $975 per year.At the endof each year she invests her years savings at 15%p.a. compound interest.How much will her investment be worth at the end of 25 years?

 

[shady145]

Please can anyone help with these qestions?

1. At the start of 1997 a country town town in NSW had a population of 28000.It was estimated that this wuld increase each year by 9% of its population at the start of that year.What is the estimated population for the start of the year 2001?

in 1998 the population will be 109% of 1997
so population=1.09x28000=30520
in 1999 the population will grown another 9% so 109% of that of 1998
population(year 1999)=1.09x30520=33266.8
pop(years 2000)=1.09x33266.8=36260.812
pop(2001)=1.09x36260.812=39524.28508
there thats as simple as i cna make it

 

[PC]

1. At the start of 1997 a country town town in NSW had a population of 28000.It was estimated that this would increase each year by 9% of its population at the start of that year. What is the estimated population for the start of the year 2001?

This is just a compound interest question over 4 years.
A = P(1 + r)ⁿ
= 28000 x (1 + 0.09)⁴
= 28000 x (1.09)⁴
= 39524.28508
.: Estimated population at start of 2001 is about 39500.

2. Adriana is a student and saves $975 per year. At the end of each year she invests her years savings at 15%p.a. compound interest. How much will her investment be worth at the end of 25 years?

This is a future value question - you can tell its an annuity because Adriana saves the same amount each year, not just a single amount.

A = M { (1+r)ⁿ – 1 / r }
= 975 { (1+0.15)²⁵ – 1 / 0.15 }
= 975 { (1.15)²⁵ – 1 / 0.15 }
= 975 { 31.91895262 / 0.15 }
= $207 473.19