MTH 245 Matrices, Transformations and Mathematics of Finance 1. Suppose you have

Question

MTH 245 Matrices, Transformations and Mathematics of Finance 1. Suppose you have just bought a house for $420,000. After putting a down payment of $30,000 you take out a mortgage for the remaining S390,000 at an interest rate of 47% per year. Use matrices to determine the monthly payment that will pay off this loan in a. 30 years (360 monthly installments). b. 20 years (240 monthly installments). c. 15 years (180 monthly installments). 2. Use matrices to determine the amount outstanding on loan (a) after a period of a. five years. b. ten years. 3. Suppose you buy a new car for $30,000. After putting a down payment of $2,000 you take out a loan for the remaining $28,000 at an interest rate of 1 .9% per year. a. Use matrices to determine the monthly payment that will pay off this loan in 4 years. b. Use matrices to determine what the outstanding balance would have been on the above loan after 12 payments. 4. Find the future value of an ordinary annuity involving deposits of $300 per month at an interest rate of 5.5% per year after a. ten years. b. twenty-five years 5. Starting today, you decide to deposit $450 per month in an ordinary annuity that earns annual interest of 7.1%. After 40 years you retire and your contributions stop. a. How much is the annuity worth at the time you retire? b. Suppose you keep withdrawing $3,000 a month in retirement for a period of 30 years. Would you have run out of funds by then?

Explanation / Answer

EMI = [P x R x (1+R)^N]/[(1+R)^ (N-1)],

In this formula the variables stand for:

EMI is the equated monthly installment
P is the principal or the amount that is borrowed as a loan
R is the rate of interest that is levied on the loan amount (the interest rate should be a monthly rate)
N is the tenure of repayment of the loan or the number of monthly installments that you will pay (tenure should be in months)

Here P = 390000

R = 4.7

N = 360 , 240, 180

So

EMI = 2023 $ (N=360)

EMI = 2510 $ (N=240)

EMI = 3023 $ (N=180)

(2)

For N = 360

in 5 year total remaining payment = 2023 * (30-5) * 12 = 606900 $

in 10 year total remaining payment = 2023 * (30-10) * 12 = 485520 $

For N = 240

in 5 year total remaining payment = 2510 * (20-5) * 12 = 451800 $

in 10 year total remaining payment = 2510 * (20-10) * 12 = 301200 $

For N = 180

in 5 year total remaining payment = 3023 * (15-5) * 12 = 362760 $

in 10 year total remaining payment = 3023 * (15-10) * 12 = 181380 $

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