Question

1. A company takes out a loan of $50,000 at 6 % interest. The term of the loan is seven years, with equal payments of $5000 at the end of the first through sixth years. The balance of the loan is due as a "balloon payment" at the end of the seventh year. Draw a cash flow diagram for this problem, assigning proper symbols to any unknown values. DO NOT solve for the unknowns.

Answer 1

Loan amount or present value of all payment = 50000

interest rate (i)=6%

Yearly payment for 1-6 years (P) = 5000

Number of years of yearly payment (n) =6

Balloon payment is to be paid at end of year (n) =7

Loan amount formula = PV of annual payment + PV of balloon payment

50000 = P*(1-(1/(1+i)^n))/i + Balloon payment/(1+i)^n

50000 = 5000*(1-(1/(1+6%)^6))/6% + (B/(1+6%)^7)

50000 = 24586.62163 + (B*0.6650571136)

50000 - 24586.62163 = (B*0.6650571136)

25413.37837/0.6650571136 = B

B =38212.3247

So balloon payment at end of 7th year is $38212.32

Cash flow diagram

Year 0 ......Year 1.........Year 2.......Year 3....Year 4......Year 5.......Year 6...........Year 7

|-----------------|----------------|--------------|--------------|-------------|------------|----------------|

-50000 50000 50000 5000 50000 5000 5000   38212.32