# problem #4

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Assume that you are nearing graduation and have applied for a job with a local bank.  As part of the bank’s evaluation process, you have been asked to take an examination that covers several financial analysis techniques.  The first section of the test addresses time value of money analysis.  See how you would do by answering the following questions.

1. Draw time lines for (a) a \$2000 lump sum cash flow at the end of year 4, (b) an ordinary annuity of \$1000 per year for 5 years, and (c) an uneven cash flow stream of -\$450, \$1000, \$650, \$850 and \$500 at the end of years 0 through 4.
2. What is the future value of an initial \$1000 after 5 years if it is invested in an account paying 5% annual interest?
3. What is the present value of \$1000 to be received in 4 years if the appropriate interest rate is 5%?
4. We sometimes need to find out how long it will take a sum of money (or anything else) to grow to some specified amount.  For example, if a company’s sales for 2020 is \$1000 and expected to grow at a rate of 10% per year, how long will it take sales to double?
5. If you invested \$10,000 in an investment account and you expect it to double in 4 years, what interest rate must it earn?
6. What is the future value of a 5-year ordinary annuity of \$1000 if the appropriate interest rate is 5%? What is the present value of the annuity?
7. What is the future value of \$1000 after 4 years under 10% annual compounding?  Semiannual compounding?  Quarterly compounding?  Monthly compounding?  Daily compounding
8. What is the effective annual rate (EAR or EFF%)?  What is the EFF% for a nominal rate of 5%, compounded semiannually?  Compounded quarterly?  Compounded monthly?  Compounded daily?
9. Construct an amortization schedule for a \$1,000, 12% annual rate loan with 4 equal installments. What is the annual interest expense for the borrower, and the annual interest income for the lender, during Year 2?
10. Suppose on January 1 you deposit \$1000 in an account that pays a nominal, or quoted, interest rate of 12%, with interest added (compounded) daily.  How much will you have in your account on October 1, or 9 months later?
11. You want to buy a car, and a local bank will lend you \$10,000. The loan would be fully amortized over 6 years (72 months), and the nominal interest rate would be 10%, with interest paid monthly. What is the monthly loan payment?
12. While Mary Corens was a student at the University of Tennessee, she borrowed \$20,000 in student loans at an annual interest rate of 5%. If Mary repays \$200 per year, then how long (to the nearest year) will it take her to repay the loan?

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