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1. Skip Town borrowed $20,000 at a rate of 12% compounded monthly. He was suppos

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Question

1. Skip Town borrowed $20,000 at a rate of 12% compounded monthly. He was supposed to pay it back in 60 equal payments over the next 5 years. However, immediately after his 30th payment, Skip decided to pay off the balance. How much did he have to pay?

2. N. Gin Earring company stock has the following potential of going up or down over a 12-month period.

Up/Down Potential       Probability

80%                            0.4

50%                            0.3

-20%                            0.2

-60%                            0.1

What is the expected rate of return after the 12-month period?

Explanation / Answer

1. Loan borrowed = $ 20,000; Rate of interest = 12% compounded monthly= 1% per month = 0.01 ; Time = 5 years = 60 periods; Let C be the monthly payment

    Montly payment = 20,000 = C x (1-1/(1+r)n/r) = C x (1-1/(1+0.01)60/ 0.01

                                            = C x (1-1/1.82)/0.01

                                             =C x ( 1.82 - 1/1.82)/0.01

                                            = C x (0.82/1.82)/0.01

                                           = C x (0.82/1.82 x 1/0.01) = 45.05

                                C = 20,000/45.05 = $443.95 per month

Total amount paid in 30 instalments = 443.95 x 30 = $13,318.5

Present Value of $13,318.5 (t=30, r = 0.01 monthly) = 13,318.5/(1+0.01)30= 13,318.5/1.35 = $9865.55

So for, Skip paid the principal amount $ 9865.55

So, the balance amount amount to be paid = 20,000 - 9865.55 = $10,134.45

2. Expected rate of return after 12 months = (80% x 0.40) + (50% x 0.3) + (-20% x 0.2) + (-60% x 0.1) = 32% + 15% - 4% - 6% = 37%