Calculation of Cash Down Price

To calculate the cash down price of the house, we need to consider the down payment made initially and the subsequent yearly payments made for 25 years.

Initial Down Payment:
The person paid $20,000 in cash as a down payment when buying the house.

Yearly Payments:
The person also made yearly payments of $4,000 for 25 years.

Interest Rate:
The interest rate for the house is given as 5% per annum compounded annually.

Now, let's calculate the total amount paid by the person over 25 years.

Yearly Payments Calculation:
The yearly payment made by the person is $4,000 for 25 years, so the total amount paid through yearly payments is:
$4,000 x 25 = $100,000

Interest Calculation:
To calculate the interest, we need to consider the principal amount, which is the down payment plus the total amount paid through yearly payments.
Principal amount = Down payment + Total yearly payments
Principal amount = $20,000 + $100,000 = $120,000

To calculate the interest earned on the principal amount over 25 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Total amount including interest
P = Principal amount
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years

In this case:
P = $120,000
r = 5% = 0.05 (as a decimal)
n = 1 (compounded annually)
t = 25

A = $120,000(1 + 0.05/1)^(1x25)
A = $120,000(1.05)^25
A ≈ $320,713.42

Cash Down Price:
The cash down price of the house is the total amount paid by the person, including the down payment and the interest earned over 25 years.
Cash Down Price = Down payment + Total interest
Cash Down Price = $20,000 + ($320,713.42 - $120,000)
Cash Down Price = $20,000 + $200,713.42
Cash Down Price ≈ $220,713.42

Therefore, the cash down price of the house is approximately $220,713.42.