Mr. Bill purchased a new house at $100,000. He paid $25,000 down and agreed to pay the rest over the next 30 years in 30 equal end-of –year payments plus 8 percent compound interest on the unpaid balance. What will these equal payments be?

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The first step in answering this question is to calculate the total amount of money that Mr. Bill will need to pay over the 30-year period. This can be done by taking the purchase price ($100,000) and subtracting the down payment ($25,000). This leaves a remaining balance of $75,000 that needs to be paid back over 30 years at 8 percent compound interest.

In order to figure out what these equal payments would be every year for 30 years we must use an annuity formula with an exponential growth factor. The equation is: PMT = (PV * i) / [1 – (1 + i)^-n], where PV is the present value (balance owing), n is number of periods (30 years), and i is rate per period (8% divided by 12 which provides a monthly rate). After plugging in all necessary values, we find that each annual payment will be $6,958.50.

These payments are made up of both principal repayment as well as interest on any outstanding balance from previous payments. As such, earlier payments will have higher amounts attributed towards interest while later payments contain more principal repayment due to compounding interest factored into each payment calculation. In other words, Mr. Bill’s early payments may see larger chunks going towards paying off the debt while later payments might contain fractions of a dollar still owed due to compounded interests over time before it reaches zero after 30 years if he makes all his required annual installments on time each year as agreed upon in his contract agreement with lender/creditor.