Project. Mortgage Problem

Each group will select own house now on market with the photo and sales price.

You will have to check current APR that your bank provides for different terms

$($select either $30$ or $15$ years mortgage$).$ You will need to calculate your monthly

payment using corresponding formula $.$ Then you will use Excel to make

amortization table with and without prepayments $($You make additional payments

toward your principal, so your loan will be paid off faster$).$ website to check you calculations and you also can try the following

example first.

Assume that you are taking $15$ years mortgage of $$200000$ with the corresponding APR

$(6\mathrm{.}25\%).$ Answer the following questions:

$1.$ Financial calculator gives a schedule for your current

mortgage and loan amortization curve $($blue graph$).$ Blue graph shows how you

can pay your mortgage. Obtain each value analytically using formulas in your

book $($present value of the annuity, future value of the annuity, etc$)$

a$.$ $$1714\mathrm{.}85$ of your monthly payment

b$.$ $$270,936\mathrm{.}17$ of your total payment

c$.$ $$70,936\mathrm{.}17$ of your total interest

$9$

$2.$ In the same graph, the red curve represents your loan amortization if you make

addition payments toward your principal $($annual or monthly$).$ You can pay less

interest and pay off your debt sooner than $15$ years if you start making additional

payments $($prepayments$)$ toward your principal. Based on your red curve and

using mathematical formulas explain how the red curve was obtained. Determine

the impact of any principal prepayment.

$3.$ Let us assume that you want to pay off your mortgage in $5$ years. How much your

annual prepayments must be$?$ Confirm your answer

website and using mathematical formulas.

$4.$ Suppose that you are taking a business loan in order to expand your production.

Your business loan equals to your project mortgage amount at the same APR and

initially for the same number of the years. Instead of making monthly payments,

you are now allowed to make five annual equal payments. How much such equal

payment will be$?$ Use present value formula; show your work and payment

diagram.

$5.$ Use Excel spreadsheet to create your mortgage amortization table with

a$)$ no prepayment

b$)$ With monthly prepayments

c$)$ With only five annual payments.