Prepared by a small team of First Year Editorial Board Members, these problem sets are the perfect way for you guys to test your skills and quick thinking. Try solving these amazingly structured questions and see how good you are!
A company expects a series of 24 monthly receipts of $3,600 each. The first payment will be received 1 month from today. Determine the present value of this series assuming an interest rate of 12% per year compounded semiannually.
A Foundation announces that it will be offering one MIT scholarship every year for an
indefinite number of years. The first scholarship is to be offered exactly one year from
now. When the scholarship is offered, the student will receive $20,000 annually for a
period of four years, beginning from the date the scholarship is offered. This student
is then expected to repay the principal amount received ($80,000) in 10 equal annual
installments, interest-free, starting one year after the expiration of her scholarship.
This implies that the foundation is really giving an interest-free loan under the guise of
a scholarship. The current interest is 6% for all maturities and is expected to remain
(a) What is the PV of the first scholarship?
(b) The foundation invests a lump sum to fund all future scholarships. Determine
the size of the investment today.
An Individual Retirement Account (IRA) allows you to set aside a limited amount
of money each year for retirement. These funds will have a special tax status that depends on several
factors. (These factors include your marital status, whether you
have other sources of retirement savings, your income, etc.)
Suppose that you have $2,000 in pretax income to contribute to the IRA at the end of
each year (starting with the end of the current year, i.e., year 1). You will retire in 30
years, and your marginal tax rate will be 28% for all years. Suppose that the account
returns a fixed 6% each year until you retire. For simplicity, assume that you withdraw
all money at your retirement, and any tax-deferred income is taxed at that time.
(a) How much money will you have in year 30 if neither the contribution nor the interest
income is tax-deferred? (In this case, you can withdraw the money without
paying any additional tax at year 30.)
(b) How much money will you have in 30 years if the contribution is not tax-deferred
but the interest income is? (In this case, only the cumulative interest is taxed at
(c) How much money will you have in 30 years if both the contribution and the
interest income are tax-deferred?
(d) Would you expect the benefit of tax deferral to increase or decrease as the tax
rate increases? Why?