Question

chapter 2 - quiz#1: present value
started: sep 15 at 7:23pm
quiz instructions
unlimited time & attempts
question 1
jeff purchased a home five years ago. if it appreciated 5% annually and is worth $161,802 today, what was his purchase price? (keep 2 decimal places)
2 pts

Explanation:

Step1: Identify the present - value formula

The formula for present value with compound - interest is $PV=\frac{FV}{(1 + r)^n}$, where $PV$ is the present value, $FV$ is the future value, $r$ is the interest rate per period, and $n$ is the number of periods. Here, $FV = 161802$, $r=0.05$, and $n = 5$.

Step2: Substitute values into the formula

$PV=\frac{161802}{(1 + 0.05)^5}=\frac{161802}{1.05^5}$.

Step3: Calculate $1.05^5$

$1.05^5=1.05\times1.05\times1.05\times1.05\times1.05 = 1.27628$.

Step4: Calculate the present value

$PV=\frac{161802}{1.27628}\approx126775.47$.

Answer:

$126775.47$