A certain house costs $285,000. It is estimated that the price of the house will rise 5% each year. If the prices actually rise at that rate, what will the price, P, of the house equal in y years?
a. Fill in a table for the price of the house in each year after the start (year 0):
previous year's value*1.05. The first three are (1) 299,250 (2) 314,212.5 (3) 329,923.125
To fill in the table for the price of the house in each year after the start (year 0), we can use the formula for compound interest. The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial amount)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years the money is invested/borrowed for
In this case, the initial price of the house is $285,000, and the annual interest rate (increase) is 5% or 0.05. Since the price of the house is estimated to rise each year, we can assume the interest is compounded annually, so n = 1. The number of years the price will be calculated for is y.
Let's fill in the table for the price of the house in each year after the start (year 0) using different values of y:
Year 0: P = $285,000 (starting price)
Year 1: P = $285,000 * (1 + 0.05)^1
Year 2: P = $285,000 * (1 + 0.05)^2
Year 3: P = $285,000 * (1 + 0.05)^3
...
Year y: P = $285,000 * (1 + 0.05)^y
Simply plug in different values of y into the formula to calculate the price of the house in each year.