the formula S=c(1+r)^2 models inflation, where C= the value today, r=the annual inflation rate, and S= the inflated value t years from now use this formula to solve the problems: If the inflation rate is 6% how much will a house now worth $465,000 be worth in 10 years? If the inflation rate is 3% how much will a house now worth $510,000 be worth in 5 years?
(1+r)^t NOT (1+r)^2 except for two years
465,000 (1.06)^10
= 465,000 (1.79)
= 832,744.18
now you do the rest
To solve these problems, we will use the formula for inflation: S = C(1 + r)^t, where C is the value today, r is the annual inflation rate, t is the number of years, and S is the inflated value t years from now.
Problem 1:
If the inflation rate is 6% and a house is currently worth $465,000, we need to find the value of the house in 10 years.
First, we substitute the given values into the formula:
C = $465,000 (value today)
r = 0.06 (6% as a decimal representing the annual inflation rate)
t = 10 (number of years we want to calculate for)
So the formula becomes:
S = 465,000(1 + 0.06)^10
To solve this, we need to calculate (1 + 0.06)^10 first, which is equal to approximately 1.790847.
Now we substitute this value back into the formula:
S = 465,000 * 1.790847
Calculating this, we find that S ≈ $831,901.55.
Therefore, the house will be worth approximately $831,901.55 in 10 years.
Problem 2:
If the inflation rate is 3% and a house is currently worth $510,000, we need to find the value of the house in 5 years.
Using the same formula:
C = $510,000 (value today)
r = 0.03 (3% as a decimal representing the annual inflation rate)
t = 5 (number of years we want to calculate for)
So the formula becomes:
S = 510,000(1 + 0.03)^5
Calculating (1 + 0.03)^5, we find the value to be approximately 1.159274.
Now we substitute this value back into the formula:
S = 510,000 * 1.159274
Calculating this, we find that S ≈ $590,908.75.
Therefore, the house will be worth approximately $590,908.75 in 5 years.