In this scenario, you're trying to find out the annual interest rate for the loan you are taking from the seller to purchase a house.
First, we need to find out the total amount of the loan, which would be the cost of the house minus the down payment. So:
360 million PYG - 105 million PYG = 255 million PYG
This is the amount you'll have to pay back over 8 years, at a rate of 4 million PYG per month.
The total amount you will repay over 8 years is:
4 million PYG/month * 12 months/year * 8 years = 384 million PYG
Now we have a loan of 255 million PYG that becomes 384 million PYG after 8 years. To find the yearly interest rate, we need to set up an equation and solve it. But remember, it's a bit complex because this is an amortizing loan, not simple interest.
The formula for an amortizing loan payment is:
P = [r*PV] / [1 - (1 + r)^-n]
P = periodic payment = 4 million PYG PV = present value = 255 million PYG r = periodic interest rate n = number of periods = 8 years * 12 months/year = 96 months
Substituting the values we know:
4 = [r * 255] / [1 - (1 + r)^-96]
We have to solve this equation for r, which is quite challenging without numerical methods. This is typically done using software, online calculators, or spreadsheets with built-in functions that can handle such calculations.
To make it more manageable, I would suggest using a financial calculator or a software tool to calculate it. These tools are designed to handle such calculations and can provide the answer quickly and accurately.
Please note that the periodic interest rate r should be multiplied by 12 to get the annual rate.