Question

The formula S=C(1+r) models inflation, where C = the value today, r = the annual inflation rate, and S = the inflated value t years from now. a. If the inflation rate is 6%, how much will a house now worth $465,000 be worth in 10 years? b. If the inflation rate is 3%, how much will a house now worth $510,000 be worth in 5 years?

Answer 1

The formula that models inflation is

`S=C(1+r)^t`

C= value today

r= annual inflation rate → usually this value is given as a percentage, but when you input the value in the formula, you have to express it as a decimal value.

S= the inflated value given a determined period of time (t).

a.

r=6%=6/100=0.06/year

C=$465000

t=10 years

`\begin{gathered} S=465000(1+0.06)^(10) \\ S=832744.1789 \end{gathered}`

The price of the house in 10 years at an inflation rate of 6% will be S=$832744.18

b.

r=3%=3/100=0.03/year

C=$510000

t=5years

`\begin{gathered} S=510000(1+0.03)^5 \\ S=437954.3531 \end{gathered}`

The price of the house in 5 years at an inflation rate of 3% will be S=$437954.35