Time Value of Money Assignment – 200 points
Complete the following problems by providing the answer and the variables used to find the answer (PV, FV, N, I, PMT). You are not required to include the formulas. You are only required to include a timeline when asked but feel free to use them on all problems.
1. Future Value If you deposit $2000 in a bank account that pays 6% interest annually, how much will be in your account after 5 years? (Include a timeline – worth 15 points)
2. What is the balance in an account at the end of 10 years if $2,500 is deposited today and the account earns 4% interest, compounded annually? quarterly? (worth 10 points)
3. Suppose you want to have $0.5 million saved by the time you reach age 30 and suppose that you are 20 years old today. If you can earn 5% on your funds, how much would you have to invest today to reach your goal? (worth 10 points)
4. Present Value What is the present value of a security that will pay $29,000 in 20 years if securities of equal risk pay 5% annually? (Include a timeline – worth 15 points)
5. If you deposit $10 in an account that pays 5% interest, compounded annually, how much will you have at the end of 10 years? 50 years? 100 years? (worth 10 points)
6. Complete the following, solving for the present value, PV. For this problem, you only need to enter the value into the column/no need to show work or variables used. (worth 10 points)
Case
Future
value
Interest
ate
# of
periods
Present
Value
A
$10,000
5%
5
B
$563,000
4%
20
C
$5,000
5.5%
3
7. Finding the Required Interest Rate Your parents will retire in 19 years. They cu
ently have $350,000 saved, and they think they will need $800,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don’t save any additional funds? (worth 10 points)
8. Time for a Lump Sum to Double If you deposit money today in an account that pays 4% annual interest, how long will it take to double your money? (worth 10 points)
9. Time to Reach a Financial Goal You have $33,556.25 in a
okerage account, and you plan to deposit an additional $5,000 at the end of every future year until your account totals $220,000. You expect to earn 12% annually on the account. How many years will it take to reach your goal? (worth 10 points)
10. Future Value: Annuity versus Annuity Due What is the future value of a 5%, 5-year ordinary annuity that pays $800 per year? If this was an annuity due, what would the future value be? (Include a timeline - worth 15 points)
11. Present Value: Ordinary Annuity Find the present value of this ordinary annuity, discounting occurs once a year: $300 per year for 6 years at 4%. Include a timeline - worth 15 points)
12. Present and Future Values of a Cash Flow Stream An investment will pay $150 at the end of the next 3 years, $250 at the end of Year 4, $300 at the end of Year 5 and $500 at the end of Year 6. If other investments of equal risk earn 11% annually, what is its present value? Its future value? (worth 20 points)
13. Loan Amortization and EAR You want to buy a car, and a local bank will lend you $40,000. The loan will be fully amortized over 5 years (60 months) and the nominal interest rate will be 8% with interest paid monthly. What will be the monthly loan payment? What will be the loan’s EAR (Effective Annual Rate)? (worth 10 points)
14. Present and Future Value for Different Periods Find the following values. (Each part worth 5 points; 20 points total)
a. An initial $600 compounded for 1 year at 6%
. An initial $600 compounded for 2 years at 6%
c. The present value of $600 due in 1 year at a discount rate of 6%
d. The present value of $600 due in 2 years at a discount rate of 6%
15. Present and Future Values for Different Interest Rates Find the following values. Compounding/discounting occurs annually. (Each part worth 5 points; 20 points total)
a. An initial $200 compounded for 10 years at 4%
. An initial $200 compounded for 10 years at 8%
c. The present value of $200 due in 10 years at 4%
d. The present value of $1870 due in 10 years at 8% and 4%
2