4. (Annuity payments) Mr. Bill S. Preston, Esq. purchased a new house for $90,00

Question

4. (Annuity payments) Mr. Bill S. Preston, Esq. purchased a new house for $90,000. He paid $30,000 upfront and agreed to pay the rest over the next 20 years in 20 equal annual payments that include principal payments plus 11 percent compound interest on the unpaid balance. What will these equal payments be?

                a. Mr Bill S. Preston, Esq. purchased a new house for $90,000 and paid $30,000 upfront, How much does he need to borrow to purchase the house? $______(Round to the nearest cent)

                b. If Bill agrees to pay the loan over the next 20 years in 20 equal end of year payments plus 11 percent compound interest on the unpaid balance, what will these equal payments be? $_____(Round to the nearest cent)

Explanation / Answer

MB0=Total pay to be borrowed=90000-30000=$60,000

Time=T=20, interest rate=r=11%

Total of Borrowed Amount= Present value of all future pays of Annuities A obtained by discounting A at rate of interest r

MB0= A/(1+r)1+........+A/(1+r)T

MB0= A(1/(1+r)1+........+1/(1+r)T)

1/(1+r)1+........+1/(1+r)T GP with first term =1/(1+r) and common ratio=cr=1/(1+r) and no of terms=T

Sum of GP= first term*(1-crT)/(1-cr) = (1/1+r) * (1-1/(1+r)T)/(1-1/(1+r))= (1-1/(1+r)T)/(r)=  (1-1/(1+r)T)/(r)

MB0=(A/r)*(1-1/(1+r)T)

A=Equal yearly pay= (MB0*r)/(1-(1/(1+r)T)

A=Equal yearly pay= (60,000*.11)/(1-(1/(1.11)20) =$7534.54

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