#1) Time value: Annuities Marian Kirk wishes to select the better of two 10-year annuities, C and D. Annuity C is an ordinary annuity of $2,500 per year for 10 years. Annuity D is an annuity due of $2,200 per year for 10 years. a. Find the future value of both annuities at the end of year 10 assuming that Marian can earn (1) 10% annual interest and (2) 20% annual interest. c. Find the present value of both annuities, assuming that Marian can earn (1) 10% annual interest and (2) 20% annual interest.
#1) Time value:
C and D.
D is an annuity due of $2,200 per year for 10 years.
a. Find the
can earn (1) 10% annual interest and (2) 20% annual interest.
c. Find the
annual interest and (2) 20% annual interest.
#2) Retirement planning Hal Thomas, a 25-year-old college graduate, wishes to retire at
age 65. To supplement other sources of retirement income, he can deposit $2,000
each year into a tax-deferred individual retirement arrangement (IRA). The IRA will
earn a 10% return over the next 40 years.
a. If Hal makes annual end-of-year $2,000 deposits into the IRA, how much will he
have accumulated by the end of his sixty-fifth year?
b. If Hal decides to wait until age 35 to begin making annual end-of-year $2,000
deposits into the IRA, how much will he have accumulated by the end of his
sixty-fifth year?
#3) Value of a mixed stream For each of the mixed streams of cash flows shown in the
following table, determine the future value at the end of the final year if deposits are
made into an account paying annual interest of 12%, assuming that no withdrawals
are made during the period and that the deposits are made
a. At the end of each year.
b. At the beginning of each year.
Cash flow stream
Year A B C
1 $ 900 $30,000 $1,200
2 1,000 25,000 1,200
3 1,200 20,000 1,000
4 10,000 1,900
5 5,000
#4) Compounding frequency, time value, and effective annual rates For each of the
cases in the following table:
a. Calculate the future value at the end of the specified deposit period.
b. Determine the effective annual rate, EAR.
c. Compare the nominal annual rate, r, to the effective annual rate, EAR. What relationship
exists between compounding frequency and the nominal and effective
annual rates?
| Case | Amount of initial deposit |
Nominal annual rate, r |
Compounding frequency, m (times/year) |
Deposit period (years) |
| A | $2,000 | 6% | 2 | 5 |
| B | 50,000 | 12 | 6 | 3 |
| C | 1,000 | 5 | 1 | 10 |
| D | 20,000 | 16 | 4 | 6 |
#5) Deposits to accumulate future sums For each of the cases shown in the following table,
determine the amount of the equal, annual, end-of-year deposits necessary to accumulate
the given sum at the end of the specified period, assuming the stated annual interest rate.
| Case | Sum to be accumulated |
Accumulation period (years) |
Interest rate |
| A | $ 5,000 | 3 | 12% |
| B | 100,000 | 20 | 7 |
| C | 30,000 | 8 | 10 |
| D | 15,000 | 12 | 8 |
#6) Loan amortization schedule Joan Messineo borrowed $15,000 at a 14% annual
rate of interest to be repaid over 3 years. The loan is amortized into three equal, annual,
end-of-year payments.
a. Calculate the annual, end-of-year loan payment.
b. Prepare a loan amortization schedule showing the interest and principal breakdown
of each of the three loan payments.
c. Explain why the interest portion of each payment declines with the passage of
time.
#7)
investment that pays no stated interest but will return $2,000 at the end of 3 years.
a. What annual rate of return will Rishi earn with this investment?
b. Rishi is considering another investment, of equal risk, that earns an annual
return of 8%. Which investment should he make, and why?
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