Question

The house was bought for $125,000 in 1990, the overage rate is 7.85%, what year will the purchase of the house be worth 3 times the purchase price?

Answer 1

Answer: 2005

Step-by-step explanation:

Exponential function to determine the value of item after t years,

$f(x)=A(1+r)^t$ , where r= rate of growth, A=Initial value.

As per given , A = 7.85% = 0.0785

A = $125,000

Substitute all values in function, we get

$f(x)=125000(1+0.785)^t$

When f(x)= 3A , then

$3A=A(1.0785)^t\\\\\Rightarrow\ 3=(1.0785)^t$

Taking tog on both sides , we get

$\ln 3=t\ln 1.0785\\\\\Rightarrow\ t=\dfrac{\ln 3}{\ln 1.0785}\\\\\Rightarrow t=\dfrac{1.09861228867}{0.0755711868471}\approx15$

The year will be 1990+15= 2005

Hence, the required year = 2005