The value of your neighbor,s house

Question

The value of your neighbor,s house was $180,000 but increase to $210,000 over the last year. If the value keeps rising by the same dollar amount each year, what kind of change is that? If the value keeps rising by the same percent each year, what kind of change is that

Answer 1

linear, if the same amount annually

18000 to 21000

to 24000

to 27000 for the 1st 3 years

P = 1800 + 3000Y where P=price after Y number of years

exponential, if the same percent annually.

compound interest, compounded annually

18000 to 21000/ 3000/18000 = 3/18= 1/6 = about 16.7% per year increase

next year 21000+21000/6 = 21000+3500 = 24,5000

3rd year 24,500+24,500/6 = 24,500+4,086.67 = 28,586.67

4th year 28,586.67 + 28,586.67/6 =3334.72

P=A(1+1/6)^Y is an exponential function where the exponent is the variable

P=1800(1+1/6)^4 = price in 4 years at 16.7% interest

=$3334.72

Generally, the compound interest formula is written as A=P(1+r/n)^nt where r= rate of interes, n= number of compounding perioids per year, t=number of years, P=original principle, A=the amountt the principal grows to after t years at r rate of interest. If compounding is continuous, the formula reduces to P=Ae^rt where e=about 2.732,