A recent college graduate is debating how nice of a car to purchase. He/she coul

ID: 1103053 • Letter: A

Question

A recent college graduate is debating how nice of a car to purchase. He/she could splurge and buy a nicer, more luxurious car such as a 2016 Chevy Silverado, a 2016 Lexus GS 350, 2015 Maserati, or 2014 Tesla Model S for around $45,000 (after all, he/she did just graduate from college- it is a luxury well deserved, right?) Alternatively, he/she could buy a more economical vehicle, such as a 2013 Toyota Tundra, 2017 Chevy Cruze, 2016 Jeep Compass, 2016 Nissan Altima, or 2012 Ford F250 for around $15,000. To further explore the options, the student obtained a quote from the local bank. For a 5 year loan, the payment on a more expensive vehicle is $850/month, and on a more economical vehicle is $290/month.

a.If the student elects to go with the more economical car, and invest the difference between the payments in a mutual fund that yields 10% per year (compounded monthly), how much will be in the account when the student turns 50? Assume that the student purchases the first vehicle on his/her 25th birthday, and continues purchasing economical cars and investing the difference until he/she turns 50 (so the monthly payments will be consistent the entire time). Fun fact: the reason the student doesn’t contribute any more to the fund at the age of 50 is because he/she purchases a luxury car, so no longer has “extra” money to invest in this account!

b.Upon the final deposit on his/her 50th birthday, the student moves the entire amount from the mutual fund to a more conservative money market account, which has an interest rate of 3% per year (you can assume annual compounding for this portion of the analysis.) If he/she begins uniform withdrawals on his/her 65th birthday, and wanted to sustain this forever, how much would this fund contribute toward the retirement each year?

c.Comment as to whether you think the amount saved in part “a” is worth the amount you have in part “b”… i.e., do you think the increase in revenue during retirement is worth foregoing some luxuries until later in life?

Explanation / Answer

Answer:

Monthly payment for expensive car

$ 850

Monthly payment for economical car

$ 290

Difference which is invested monthly, PMT

$ 560

Annual yield compounded monthly

10%

Number of years

Number of periods

300

Final value at age 50

$7,43,026.71

Amount at 65

Interest rate annual

NPER

$ 11,57,611

Uniform withdrawals per year

$ 34,728.34

It is very much prudent to foregone luxuries to have a better retirement as to have an adequate level of financial independence and security