Problema Solution
If the average of a new home costs $210,000 today, how much will it cost in 10 years if the price increases by 5% each year?
Answer provided by our tutors
the cost today is
a = $210,000
in 1 year the cost will increase by 5%
a + 0.05*a = 1.05a
in 2 years the cost is 5% bigger then the previous year
1.05a + 0.05*1.05a = a(1.05)^2
.................
in 10 years the cost will be a*(1.05)^10
the costs form geometric sequence with first term a = $210,000 and common ratio r = 1.05
in 10 years the cost will be a*r^10
a*(1.05)^10 = 210000(1.05)^10 = $342,067.87