Math 1050 Mortgage Project

Transcription

1 Math 1050 Motgage Poject Name Due date: In this poject we will examine a home loan o motgage. Assume that you have found a home fo sale and have ageed to a puchase pice of $201,000. Down Payment: You ae going to make a 10% down payment on the house. Detemine the amount of you down payment and the balance to finance. Down Payment Motgage Amount Pat I: 30 yea Motgage Monthly Payment: Calculate the monthly payment fo a 30 yea loan (ounding up to the neaest cent) by using the following fomula. Show you wok. [PMT is the monthly loan payment, P is the motgage amount, is the annual pecent ate fo the loan in decimal, and Y is the numbe of yeas to pay off the loan.] Fo the 30 yea loan use an annual inteest ate of 4.975%. P( 1 2) P M T = 1 2 Y 1 1+ ( ) 1 2 Show wok hee Monthly Payment fo a 30 yea motgage Note that this monthly payment coves only the inteest and the pincipal on the loan. It does not cove any insuance o taxes on the popety. Amotization Schedule: In ode to summaize all the infomation egading the amotization of a loan, constuct a schedule that keeps tack of the payment numbe, the pincipal paid, the inteest, and the unpaid balance. A speadsheet pogam is an excellent tool to develop an

2 amotization schedule. We can use a fee amotization speadsheet on the web. The web addess is: Ente the amount of the loan, i.e. the selling pice minus the down payment, the inteest ate, and the appopiate numbe of yeas. Check the box to show the schedule. Amotization Schedule monthly payment fo a 30 yea motgage (Note: if this is moe than 2 o 3 cents diffeent fom you calculation, check you numbes!) Total inteest paid ove 30 yeas Total amount paid Notice that the amount of the payment that goes towads the pincipal and the amount that goes towads the inteest ae not constant. What do you obseve about each of these values? Numbe of fist payment when moe of payment goes towad pincipal than inteest As aleady mentioned, these payments ae fo pincipal and inteest only. You will also have monthly payments fo home insuance and popety taxes. In addition, it is helpful to have money left ove fo those little luxuies like electicity, unning wate, and food. As a wise home owne, you decide that you monthly pincipal and inteest payment should not exceed 35% of you monthly take-home pay. What minimum monthly take-home pay should you have in ode to meet this goal? Show you wok fo making this calculation. Show wok hee Minimum monthly take home pay =.

3 It is also impotant to note that you net o take-home pay (afte taxes) is less than you goss pay (befoe taxes). Assuming that you net pay is 73% of you goss pay, what minimum goss annual salay will you need to make to have the monthly net salay stated above? Show you wok fo making this calculation. Show wok hee. Minimum goss annual salay = Pat II: Selling the House Let's suppose that afte living in the house fo 10 yeas, you want to sell. The economy expeiences ups and downs, but in geneal the value of eal estate inceases ove time. To calculate the value of an investment such as eal estate, we use continuously compounded inteest. Find the value of the home 10 yeas afte puchase assuming a continuous inteest ate of 4%. Use the full puchase pice as the pincipal. Show you wok. Show wok hee. Value of home 10 yeas afte puchase

4 Assuming that you can sell the house fo this amount, use the following infomation to calculate you gains o losses: Selling pice of you house Oiginal down payment Motgage paid ove the ten yeas The pincipal balance on you loan afte ten yeas Do you gain o lose money ove the 10 yeas? How much? Show you amounts and summaize you esults: Pat III: 15 yea Motgage Using the same puchase pice and down payment, we will investigate a 15 yea motgage. Monthly Payment: Calculate the monthly payment fo a 15 yea loan (ounding up to the neaest cent) by using the following fomula. Show you wok! [PMT is the monthly loan payment, P is the motgage amount, is the annual pecent ate fo the loan in decimal, and Y is the numbe of yeas to pay off the loan.] Fo the 15 yea loan use an annual inteest ate of 4.735%. P( 1 2) P M T = 1 2 Y 1 1+ Show wok hee. ( ) 1 2 Monthly Payment fo a 15 yea motgage =

5 Use the amotization speadsheet on the web again, this time enteing the inteest ate and numbe of payments fo a 15 yea loan. Amotization Schedule monthly payment fo a 15 yea motgage (Note: if this is moe than 2 o 3 cents diffeent fom you calculation, check you numbes!) Total inteest paid ove 15 yeas Total amount paid Numbe of fist payment when moe of payment goes towad pincipal than inteest Suppose you paid an additional $100 towads the pincipal each month. How long would it take to pay off the loan with this additional payment and how will this affect the total amount of inteest paid on the loan? [If you ae making exta payments towads the pincipal, include it in the monthly payment and leave the numbe of payments box blank.] Length of time to pay off loan with additional payments of $100 pe month Total inteest paid ove the life of the loan with additional $100 monthly payments Total amount paid with additional $100 monthly payments Compae this total amount paid to the total amount paid without exta monthly payments. How much moe o less would you spend if you made the exta pincipal payments? Pat III: Reflection Did this poject change the way you think about buying a home? Wite one paagaph stating what ideas changed and why. If this poject did not change the way you think, wite how this poject gave futhe evidence to suppot you existing opinion about buying a home. Be specific.