### Theory of interest

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Theory of Interest

NPV, IRR, Nominal and Real, Amortization, Sinking Fund, TWRR, DWRR

1. Given NPV=-1000+500v^3+800v^8 and a rate of interest of 4%, what is the NPV? Should we invest? An alternative investment with similar risks is available and returns \$550 in 3 years and \$720 in 8 years for the same \$1000 investment. Based on the NPV approach, which of the two investments should we make?

2. A project requires an initial investment of \$10,000 and it produces net cash flows of \$10,000 one year from now and \$2000 two years from now. The annual effective interest rate is 11%. Determine the project's net present value and internal rate of return.

A. 17.08%       B. 18.08          C. 19.08%       D. 20.08%       E. 21.08%

3.   A zero-coupon bond costs \$85 and it will pay \$100 in 5 years. Determine the internal rate of return for this bond.

A. 1.3%           B. 2.3%           C. 3.3%           D. 4.3%           E. 5.3%

4.  Sally lends 10,000 to Tim. Tim agrees to pay back the loan over 5 years with monthly payments payable at the end of each month. Sally can reinvest the monthly payments from Tim in a saving account paying interest at 6%, compounded monthly. The yield rate earned on Sally's investment over the five-year period turned out to be 7.45% compounded semiannually. What nominal rate of interest, compounded monthly, did Sally charge Tim on the loan?

A. 8.53%         B. 8.59%         C. 8.68%         D. 8.80%         E. 9.16%

5. The real interest rate is 5% and the inflation rate is 3%. Brian expects a payment of \$100 in one year, and subsequent payments increase by \$5 each year for 5 more years. Determine the accumulated value of these payments at time 6 years.

A. 800             B. 820             C. 840             D. 860'            E. 880

6. \$100 is invested at the beginning of each year for 10 years at 10%. The interest is reinvested at 5%. What is the total AV at the end of 10 years?

A. 1550.59      B. 1579.82      C. 1600.90      D. 1641.36      E. 1658.08

7. A deposit of 1 is made at the end of each year for 30 years into a bank account that pays interest at the end of each year at j per annum. Each interest payment is reinvested to earn an annual effective interest rate of j/2. The accumulated value of these interest payments at the end of 30 years is 72.88. Determine j.

A. 8.0%           B. 8.5%           C. 9.0%           D. 9.5%           E. 10.0%

8. On January 1, an investment account is worth 100. On May 1, the value has increased to 120 and D is deposited. On November 1, the value is 100 and 40 is withdrawn. On January 1 of the following year, the investment account is worth 65. The time-weighted rate of interest is 0%. Calculate the dollar-weighted rate of interest.

A. -10%           B. -5% C. 0%              D. 5%              E. 10%

9. On January 1, 1997, Brian's stock portfolio is worth \$100,000. On September 30, 1997, \$5000 is withdrawn from the portfolio, and immediately after this withdrawal the portfolio has a value of \$105,000. Twelve months later, the value of the portfolio is \$108,000, and Brian adds \$3000 worth of stock to his portfolio. On December 31, 1998, the portfolio is worth \$100,000. Calculate X, the time-weighted rate of return for Brian's stock portfolio over the two-year period.

A. X < 0.0%                            B. 0.0% < X < 0.8%               C. 0.8% < X < 1.6%

D. 1.6% < X < 2.4%               E. X > 2.4%

(Equivalent annual rate = .96%)

10. 100 is deposited into an investment account on January 1, 1998. You are given the following information on investment activity that takes place during the year:

 April 19, 1998 October 30, 1998 Value immediately prior to deposit 95 105 Deposit 2X X

The amount in the account on January 1, 1999 is 115. During 1998, the dollar-weighted rate of return is 0% and the time-weighted return is y. Calculate y.

A. -1.5%          B. -0.7%          C. 0.0%           D. 0.7%           E. 1.5%

11. Payments on a \$10,000 loan are made quarterly in arrears for 10 years. The annual effective rate of interest is 7%. Using the amortization method:

i. Find the quarterly payment

ii. Find the principal outstanding after the 6th payment.

iii. Find the total amount of interest payable on the loan.

iv. Find the interest and principal paid in the 10th payment.

12. Iggy borrows X for 10 years at an annual effective interest rate of 6%. If he pays the principal and accumulated interest in one lump sum at the end of 10 years he would pay 356.54 more in interest than if he repaid the loan with 10 level payments at the end of each year. Calculate X.

A. 800             B. 825             C. 850             D. 875             E. 900

13.  A 12-year loan of 8000 is to be repaid with payments to the lender of 800 at the end of each year and deposits of X at the end of each year into a sinking fund. Interest on the loan is charged at an 8% annual effective rate. The sinking fund annual effective interest rate is 4%. Calculate X.

A. 298             B. 330             C. 361             D. 385             E. 411

14. Sam borrowed \$1000 on January 1, 1993 to be repaid by level payments every two years beginning January 1, 1995, at an effective annual rate of interest of 9%. The amount of interest in the 4th installment is \$177.72. Determine the amount of principal in the 6th installment.

A. 25.35          B. 30.65          C. 35.95          D. 41.25          E. 46.55

15. A 20-year loan of 20,000 may be repaid under the following two methods:

i. amortization method with equal annual payments at an annual effective rate of 6.5%

ii. sinking fund method in which the lender receives an annual effective rate of 8% and the sinking fund earns an annual effective rate of j.

Both methods require a payment of X to be made at the end of each year for 20 years. Calculate j.

A. j < 6.5%                              B. 6.5% < j < 8.0%                 C. 8.0% < j < 10.0%

D. 10.0% < j < 12.0%             E. j > 12.0%

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