Time Value

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1. Assume that this year, the average wedding cost $25,000. Assuming 4%
inflation, what will it cost in 30 years?
2. At what rate must money be invested to double the money over a 10 year time
frame?
3. Suppose you need $10,000 in two years for the down payment on a new car. If
you can earn 7% annually, how much do you need to invest today?
4. You want to begin saving for your daughter’s college education and you
estimate that she will need $150,000 in 17 years. If you feel confident that you
can earn 8% compounded semiannually, how much do you need to invest today?
5. You are considering an investment that will pay you $1,000 in one year, $2,000
in two years and $3,000 in three years. If you want to earn 10% on your money,
how much would you be willing to pay?
6. What is the present value of the 25 annual payments of $50,000 offered to a
soon-to-be ex-spouse, assuming a 5% discount rate?
7. Assuming $2000 annual contributions earn a 9% return, how much will an
Individual Retirement Account (IRA) be worth in 30 years?
8. Suppose you begin saving for your retirement by depositing $2,000 per year in
an IRA starting at the end of the year. If the interest rate is 7.5%, how much will
you have in 40 years?
9. You are saving for a new house and you put $10,000 per year in an account
paying 8%. The first payment is made today. How much will you have at the end
of 3 years?
10. You are renting a storage warehouse for 6 years. The rent is $6,000 per year
payable at the beginning of each year. You want to set aside the money
necessary to meet these payments. If the money you deposit in the payment
account earns 9% compounded annually, how much do you have to deposit in the
account?
11. To purchase a new boat, you agree to pay the owner each year at the
beginning of the year for five years. The boat will cost you $25,000. If you agree
to a loan rate of 10% for the right to buy the boat in payments rather than in one
lump sum, how much are your annual payments?
12. If the present value of an investment is $78.35 and the future value is $100,
how long was the investment invested if the rate earned was 5%?
13. If the present value of a six (6) year investment is $95.00 and the future value
is $145, what rate is being earned?
14. If an investment increased in value from $30,000 to $80,000 in 5 years, what
was the annual compounded rate of growth?
15. What is the present value of a perpetuity of $5,000 invested at a rate of
12%?
16. Your cousin has just invested in a consul bond that promises to pay $200 per
year into perpetuity. She would like to know the final ending value of the bond.
17. What is the effective annual rate of interest on your credit card if the nominal
rate is 18% per year, compounded monthly?
18. You are looking at two savings accounts. One pays 5.25%, with quarterly
compounding. The other pays 5.30% with semiannual compounding. Which
account should you use?
19. If you deposit $300 today, what is the future value of the deposit five years
from now with 8% interest compounded quarterly?
20. What is the PV of $100 one year from now with 12% interest compounded
monthly?
21. What is the future value of $100 invested at the end of each year for three
years if the money is invested at 12% interest compounded quarterly?
22. What is the present value of $500 invested at the end of each year for four (4)
years if the money is invested at 8% interest compounded quarterly?
23. How long must you leave $5,000 invested at 6% compounded semiannually
for the investment to grow to $10,000?
24. What is the table factor that you would find on the present value of a $1
Annuity for 30 years and 6.5% compounded monthly?
25. If you invest $11,000 in a mutual fund today, and it grows to be $50,000 after
8 years, what compound annual rate of return did you earn?
26. Find the compound value of a $125, ten-year ordinary annuity at 6 percent
annual interest if the payment at the end of year 6 is omitted.
$125 $125 $125 $125 $125 $125 $125 $125 $125
|__________|__________|_________|__________|_________|_________|_________|_________|_________|_________|

0 1 2 3 4 5 6 7 8 9 10
27. A father is planning to provide a 20-year trust fund for his son Dominic. The
amount deposited today will remain untouched until the end of the 20th year, but
will gain interest at a rate of 8 percent compounded annually. The money will
then be transferred to another account, which pays 6 percent. The intent is that
Dominic will withdraw the money in six equal annual payments of $4,000 each
beginning at the end of year 20. The fund, which will help to pay for his higher
education will be completely depleted after six payments. What amount should
Dominic’s father deposit today?
$4,000 $4,000 $4,000 $4,000 $4,000 $4,000
|____________|____________|___________|___________|___________|___________|___________|___________|

0……………………………..20 21 22 23 24 25 26
28. You have borrowed $10,000 at 9%. Your lender requires annual payments
over a four-year period. Identify the amount of each payment.
29. You have borrowed $10,000 at 9%. Your lender requires annual payments
over a four year period. Create an amortization table for your loan. Use the
payment determined in question number 28.

 

 

Sample Solution

While a set of frameworks complement and build on each other, the delineation of the concept focuses heavily on vertical versus horizontal dimensions in a time-sliced fashion. That is, time dimension in accountability has not been of primary importance. However, it is worth noting that the time dimension is closely interrelated with a series of conceptual distinctions made in previous literature, and it may cover complementary aspects of the question concerning two sequential lines represented by administrative responsibility versus political accountability. First, the positioning of accountability actors depends on the time dimension. Civil servants usually have longer terms to serve the public interest over the long term. At the same time, they are responsible to the elected representatives of the public who tend to have “a limited time horizon” and “prefer policies that yield tangible benefits for constituents in the near term” (Posner, 2004: 137). For this reason, the priorities expressed by elected officials may be far more related to short-term issues and temporal problems instead of long-term solutions, whereas the long-lasting forms of civil service personnel would prioritize sustainable solutions to secure a long-term perspective of the citizens, both current and in the future. Second, the time frame is essential to distinguishing between two main streams of accountability. Accountability mechanisms focus predominantly on retroactive accountability for the past outcomes, while accountability as a virtue takes a proactive approach to ensuring ethical behaviors in the future. The timeline is also useful to distinguishing between ex ante accountability of the decision-making process leading up to the decision and ex post accountability where the results available from the decision already taken or where questions of compliance are identified and addressed. In other words, ex ante accountability refers to being accountable for the decision before an administrator act, while ex post accountability is suggestive of situations where administrators are accountable for the outcome of their decisions. For example, the focus of traditional bureaucratic administration is very much

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