1. Your job pays you only once a year for all the work you did over the previous
ID: 2724087 • Letter: 1
Question
1.
Your job pays you only once a year for all the work you did over the previous 12 months. Today, December 31, you just received your salary of $67,000 and you plan to spend all of it. However, you want to start saving for retirement beginning next year. You have decided that one year from today you will begin depositing 10 percent of your annual salary in an account that will earn 10.7 percent per year. Your salary will increase at 4 percent per year throughout your career.
How much money will you have on the date of your retirement 45 years from today?
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2.
You need a 25-year, fixed-rate mortgage to buy a new home for $285,000. Your mortgage bank will lend you the money at an APR of 5.8 percent for this 300-month loan. However, you can afford monthly payments of only $1,250, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment.
How large will this balloon payment have to be for you to keep your monthly payments at $1,250?
Your job pays you only once a year for all the work you did over the previous 12 months. Today, December 31, you just received your salary of $67,000 and you plan to spend all of it. However, you want to start saving for retirement beginning next year. You have decided that one year from today you will begin depositing 10 percent of your annual salary in an account that will earn 10.7 percent per year. Your salary will increase at 4 percent per year throughout your career.
Explanation / Answer
1.
Since your salary grows at 4 percent per year, your salary next year will be:
Since your salary grows at 4 percent, your deposit will also grow at 4 percent. We can use the present value of a growing perpetuity equation to find the value of your deposits today. Doing so, we find:
Since your salary grows at 4 percent per year, your salary next year will be:
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