Question

chuck ponzi has talked an elderly woman into loaning him $15,000 for a new business venture. she has, however, successfully passed a finance class and requires chuck to sign a binding contract on repayment of $15,000 with an annual interest rate of 8% over the next 5 years. Ponzi may choose to pay off the loan early if interest rates change during the next 5 years. determine the ending balance of the loan each year under the three different payment plans.        A) the discount.                                              B) the interest-only loan.                                                 C) the fully amortized loan.

Answer 1

A) The discount - where interest and principle be paid after maturity

End of 1 year = 15000*1.08 = 16200

End of 2nd year = 15000*1.08^2=17496

End of 3rd year = 15000*1.08^3=18896

ENd of 4th year = 15000*1.08^4=20407

End of 5th year = 15000*1.08^5=22040

B) The interest only- only interest is paid at the end of every year and principle at the end

End of 1 year = 15000*0.08*5+15000= 21000

End of 2nd year = 15000*0.08*4+15000=19800

End of 3rd year = 15000*0.08*3+15000=18600

ENd of 4th year = 15000*0.08*2+15000=17400

End of 5th year = 15000*0.08*1+15000=16200

C) Fully amortized loan- Equal annual payments through 5 years

Let the annual payment be x, with the present value formula we need to calculate x

15000 = (x/0.08 )(1-1/1.08^5) ==> x = 3756.85

Therefore, annual payment each year = 3756.85