A mortgage can take up to 25 years to pay off. Taking a $250,000 home, calculate the month-end payment for 15-, 20-, and 25-year periods usi

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A mortgage can take up to 25 years to pay off. Taking a $250,000 home, calculate the month-end payment for 15-, 20-, and 25-year periods using semi-annually compounded interest rates of 4%, 5.5%, and 7% for each period. What do you observe from your calculations?

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Eirian 4 years 2021-07-31T21:21:55+00:00 1 Answers 10 views 0

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    2021-07-31T21:23:11+00:00

    Answer:

    a-1. Using semi-annually compounded interest rates of 4%, or 0.04, we have:

    M15 = $2,389.13

    M20 = $2,091.10

    M25 = $1,929.54

    a-2. Using semi-annually compounded interest rates of 5.5%, or 0.055

    M15 = $2,841.49

    M20 = $2,580.47

    M25 = $2,450.28

    a-3. Using semi-annually compounded interest rates of 7%, or 0.07

    M15 = $3,329.35

    M20 = $3,108.80

    M25 = $3,009.40

    b-1. It can be observed that there is a negative relationship between the month-end payment and the payment period.

    b-2. It can be observed that there is a positive relationship between the month-end payment and the semi-annually compounded interest rate.

    Step-by-step explanation:

    The month-end payment for each period can be calculated using the formula for calculating the present value (PV) of an ordinary annuity as follows:

    Mn = PV / ((1 – (1 / (1 + r))^n) / r) …………………………………. (1)

    Where;

    Mn = month-end payment for a particular year period = ?

    PV = Present value or home value = $250,000

    r = Monthly interest rate = semiannual interest rate / 6 months

    n = number of months = Number of years * 12 months

    Using equation (1), we have:

    a. Calculate the month-end payment for 15-, 20-, and 25-year periods using semi-annually compounded interest rates of 4%, 5.5%, and 7% for each period.

    a-1. Using semi-annually compounded interest rates of 4%, or 0.04

    M15 = $250,000 / ((1 – (1 / (1 + (0.04/6)))^(15*12)) / (0.04 / 6)) = $2,389.13

    M20 = $250,000 / ((1 – (1 / (1 + (0.04/6)))^(20*12)) / (0.04 / 6)) = $2,091.10

    M25 = $250,000 / ((1 – (1 / (1 + (0.04/6)))^(25*12)) / (0.04 / 6)) = $1,929.54

    a-2. Using semi-annually compounded interest rates of 5.5%, or 0.055

    M15 = $250,000 / ((1 – (1 / (1 + (0.055/6)))^(15*12)) / (0.055 / 6)) = $2,841.49

    M20 = $250,000 / ((1 – (1 / (1 + (0.055/6)))^(20*12)) / (0.055 / 6)) = $2,580.47

    M25 = $250,000 / ((1 – (1 / (1 + (0.055/6)))^(25*12)) / (0.055 / 6)) = $2,450.28

    a-3. Using semi-annually compounded interest rates of 7%, or 0.07

    M15 = $250,000 / ((1 – (1 / (1 + (0.07/6)))^(15*12)) / (0.07 / 6)) = $3,329.35

    M20 = $250,000 / ((1 – (1 / (1 + (0.07/6)))^(20*12)) / (0.07 / 6)) = $3,108.80

    M25 = $250,000 / ((1 – (1 / (1 + (0.07/6)))^(25*12)) / (0.07 / 6)) = $3,009.40

    b. What do you observe from your calculations?

    Two things can be observed from the calculations:

    b-1. At a particular semi-annually compounded interest rate, the month-end payment decreases as the payment period increases. This implies that there is a negative relationship between the month-end payment and the payment period.

    b-2. At a particular payment period, the month-end payment increases as the semi-annually compounded interest rate increases. This implies that there is a positive relationship between the month-end payment and the semi-annually compounded interest rate.

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