Problem: Emily Smith just received a promotion at work that increased her annual salary to $42,000. She is eligible to participate in her employer's 401(k) retirement plan to which the employer matches, dollar for dollar, workers' contributions up to 5% of salary. However, Emily wants to buy a new $25,000 car in 3 years, and she wants to have enough money to make a $10,000 down payment on the car and finance the balance. Fortunately, she expects a sizable bonus this year that she hopes will cover that down payment in 3 years.
A wedding is also in her plans. Emily and her boyfriend, Paul, have set a wedding date two years in the future, after he finishes medical school. In addition, Emily and Paul want to buy a home of their own in 5 years. This might be possible because two years later, Emily will be eligible to access a trust fund left to her as an inheritance by her late grandfather. Her trust fund has $80,000 invested at an interest rate of 5%.
Question: Suppose that Emily and Paul purchase a $200,000 home in 5 years and make $40,000 down payment immediately. Find the monthly mortgage payment assuming that the remaining balance is financed at a 3% fixed rate for 15 years. What if its mortgage term is 30 years?
What can you conclude about the relationship between the mortgage term and the amount of the monthly payment? From Question, is the monthly payment with the 30-year term half as large as the monthly payment with the 15-year term? Explain.