1. You just got your first “real” job and though you love it, you want to think about retirement. You
have a goal of retiring in in 35 years with $1,000,000 dollars saved by investing. You can assume
you would have an annual return of 7.5% on your investment.
a. How much should you contribute to your investment each month to achieve your goal?
b. Your brother saved the same amount of money each month that you are contributing to your
investment (that is, your answer for part (a)), also for 35 years. However, he doesn’t trust banks or
investment companies so instead he just put the money in a coffee can in his basement. How
much money will he have at the end of 35 years?
c. How much more money will you have compared to your brother?
2. You and your significant other are soon to be married and are buying your first home! The home
price is $150,000, You saved up $10,000 for a down payment and plan to finance the rest.
a. For a 30-year fixed-rate mortgage, the annual interest rate is 3.9%. Find the monthly
mortgage payment.
b. Let’s find how much you will actually pay for your $150,000 home over the life of the
mortgage. BUT…because you didn’t put at least 20% down, you will need to pay Private
Mortgage Insurance (PMI) until the balance of the mortgage is less than 80% of the value of the
home. This will add $33.83 to your monthly payment for the first 90 payments. Include this in
your total, as well as your down payment.
c. How much more than the $150,000 price tag will you actually pay for your home?
d. Your parents have gifted you a total of $25,000 for the wedding of your dreams! But…what if
instead you had a modest wedding for $5,000 and put the remaining $20,000 towards the down
payment on your home (in addition to the $10,000 you had already saved)? How much would
your monthly payment be now?
e. And NOW how much would you pay for your $150,000 home over the life of the mortgage?
(Your down payment will be at least 20% of the value of your home, too, so now you won’t have
to pay PMI, but include your down payment.)
f. How much more than the $150,000 price tag will you actually pay for your home in this
situation?
g. You noticed that a 15-year fixed-rate mortgage has a lower interest rate: 3.1%. If you had the
down payment described in part (d), how much would the monthly payment be for this shorterterm loan?
h. And then how much would you pay for your home over the life of this 15-year loan (no PMI,
but include down payment)?
i. How much more than the $150,000 price tag will you actually pay for your home in this last
situation?
j. Compare your answers for parts (c), (f), and (i).
30-yr mortgage
3.9% APR
$10,000 down
PMI required
30-yr mortgage
3.9% APR
$30,000 down
15-yr mortgage
3.1% APR
$30,000 down
Additional cost over
the $150,000 price
of your home
c) f) i)
k. What is the moral of this home-buying story? Provide 2-3 sentences demonstrating your
comprehension of the concepts demonstrated in this example