ScholarMatic: Explanation & Answer
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Do not use
the annuity tables in the textbook to solve these problems. You are required to solve all problems in
this course using a financial calculator.
For each question you must show your work and provide the solution. For example:
You will need $80,000 annually for 20 years
during retirement. How much will you
need at retirement if you can earn a 4% rate of return?
PMT = 80,000
N = 20
I = 4
PV = 1,087,226
Rule of 72
•
Tom invested $14,500 in an account he expects will earn 4%
annually. Approximately how many years
will it take for the account to double in value? 72 divided by 4 = 18 years
•
Sam has $2,000 and he needs it to grow to $4,000 in 10
years. Assuming he adds no more money to
this fund, what rate of return would he need to earn? 8%
Present
Value
•
Calculate the present value of $50,000 to be received in 13
years assuming an annual interest rate of 7%. PV= $20,748.22
•
Calculate the present value of $30,000 to be received in 5
years assuming an annual interest rate of 10%, compounded monthly. $18,627.64
Future Value
•
Calculate the future value of $10,000 invested for 30 years
assuming an annual interest rate of 8%. the FV is 100, 626. 57
•
Calculate the future value of $15,000 invested for 18 years
assuming an annual interest rate of 11% compounded
monthly.
PV Ordinary Annuity
•
Calculate the present value of an ordinary annuity of
$12,500 received quarterly for 25
years assuming a discount rate of 6%.
•
Calculate the present value of an ordinary annuity of $5,000
received monthly for 20 years
assuming a discount rate of 10%.
PV Annuity Due
•
Calculate the present value of an annuity of $8,000 received
quarterly that begins today and continues for 20 years, assuming a discount rate
of 10%.
•
Calculate the present value of an annuity of $5,000 received
monthly that begins today and continues for 25 years, assuming a discount rate
of 12%.
FV Ordinary Annuity
•
Calculate the future value of an ordinary annuity of $4,000
paid every quarter for 10 years,
assuming an annual earnings rate of 7%.
•
Calculate the future value of an ordinary annuity of $750
paid every month for 30 years,
assuming an annual earnings rate of 14%.
FV Annuity Due
•
Calculate the future value of a quarterly annuity of $2,000 beginning
todayand continuing for 15 years, assuming an annual earnings rate of 11%.
•
Calculate the future value of a monthly annuity of $10 beginning
today and continuing for 50 years, assuming an annual earnings rate of 12%.
Net Present Value (PV Uneven Payment Series ): See
NPV Calculation Notes PowerPoint
•
Calculate the NPV of a machine which is bought for $15,000,
sold at the end of year 5 for $7,500.00, and produces the following cash flows:
Year 1 $1,000, Year 2 $900, Year 3 $850, Year 4 $600, Year 5 $500, assume the
cost of capital is 11%.
•
Calculate the NPV of a machine which is bought for $6,000,
sold at the end of year 5 for $2,000.00, and produces the following cash flows:
Year 1 $2,000, Year 2 $1,750, Year 3 $1,500, Year 4 $1,000, Year 5 $500, assume
the cost of capital is 8%.
Inflation Adjusted Return (PV of inflation-adjusted annuity
due -BEG)
Don’t forget to use the inflation adjusted
interest rate formula,
Inflation
adjusted interest rate= [(1 + interest rate) / (1 + inflation rate) – 1] x
100
•
Julie is ready to retire.
She wants to receive the equivalent of $40,000 in today’s dollars at the
beginning of each year for the next 25 years.
She assumes inflation will average 3%, and she can earn a 10% after-tax
return (compounded annually) on her investments. What lump sum does she need to invest today
to attain her goal?
•
Diane and Andy are ready to retire. They want to receive the equivalent of
$75,000 in today’s dollars at the beginning of each year for the next 30
years. They assume inflation will
average 3.5% over the long run, and they can earn a 9% after-tax return
(compounded annually) on their investments.
What lump sum do they need to invest today to attain their goal?
Internal Rate of Return (IRR)
•
Jake borrowed $18,000 from his father to purchase a
camper. Jake paid back $25,000 to his
father at the end of 6 years. What was
the average annual compound rate of interest on Jake’s loan from his father?
•
Billy purchased a certificate of deposit 5 years ago for
$1,000. If the certificate of deposit is
due today in the amount of $2,000, what is the average annual compound rate of
return assuming monthly compounding, that Billy realized on his investment?
ScholarMatic: Explanation & Answer
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