Question

Suppose you borrow $8,000 and agree to repay the loan in 4 equal installments over a 4-year period. The interest rate on the loan is 13% per year. What is the amount of the reduction in principal in year 2?

A. $1,040 B. $1,864 C. $2,690 D. $826 E. $2000

Suppose you win $100 million in lottery. The money is paid in equal annual installments of $4 million over 25 years. If the appropriate discount rate is 10%, how much is the sweepstakes actually worth today?

A. $100,000,000 B. $4,000,000 C. $36,308,160 D. $42,699,100 E. $45,537,760

To buy a new house, you must borrow $270,000. To do this, you take out a $270,000, 30-year, 9% mortgage. Your mortgage payments, which are made at the end of each year (one payment each year), include both principal and 9% interest on the declining balance. How large will your annual payments be? A. $24,334 B. $26,281 C. $25,000 D. $82,809 E. $107,651

Please show steps on how to work it out

Answer 1

1

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

8000= Cash Flow*((1-(1+ 13/100)^-4)/(13/100))

Cash Flow = 2689.55

PV after year 1

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 2689.55*((1-(1+ 13/100)^-3)/(13/100))

PV = 6350.44

PV after year 2

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 2689.55*((1-(1+ 13/100)^-2)/(13/100))

PV = 4486.44

Principal paid = PV year1 - PV year 2 = 6350.44-4486.44=1864

2

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 4000000*((1-(1+ 10/100)^-25)/(10/100))

PV = 36308160.07

Please ask remaining parts seperately, questions are unrelated, I have done one bonus