Question

Mr. Bill S.​ Preston, Esq., purchased a new house for ​$150,000. He paid ​$30,000 upfront and agreed to pay the rest over the next 10 years in 10 equal annual payments that include principal payments plus 11 percent compound interest on the unpaid balance. What will these equal payments​ be?

Answer 1

The present value of equal Loan payments (P) over the next 10 years should be equal to the amount paid on a deferred basis

Amount paid on deferred basis = $150,000 -$30,000 =$120,000

So,

P/1.11 + P/1.11^2+ ... + P/1.11^10 = 120000

The above is also the present value of an annuity of P for 10 years at 11%

So,

P/0.11*(1-1/1.11^10) = 120000

=> 5.889232* P = 120000

=> P = $20376.17

The value of equal payments is $20376.17 at the end of each year for 10 years