Lecture 3 - Interest Rates

# Lecture 3 - Interest Rates - Required Reading INTEREST...

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1 Finance - I (MGCR 341) – Prof. de Mot a INTEREST RATES 2 Finance - I (MGCR 341) – Prof. de Mot a Required Reading Chapter 5 , “ Interest Rates ” from Berk and De Marzo , Corporate Finance . 3 Finance - I (MGCR 341) – Prof. de Mot a Question Mary takes a \$1 two-year loan at a 2-year interest of 10%. What is the interest rate that Mary pays per year? Answer - After two years Mary has to pay: - The equivalent annual interest rate is: - Notice that: 1 . 1 \$ 1 1 . 1 = × % 88 . 4 1 . 1 \$ 1 ) 1 ( 2 = = × + r r () 2 / 1 2 1 . 0 1 0488 . 0 1 1 . 0 1 ) 0488 . 0 1 ( + = + + = + 4 Finance - I (MGCR 341) – Prof. de Mot a Question Mary takes a \$1 two-year loan at a interest of 5% per year. What is the interest rate that Mary pays over the two-year period? Answer - After two years Mary has to pay: - Hence the interest rate over the two-year period is: - Notice that: 1025 . 1 \$ 1 * ) 05 . 1 )( 05 . 1 ( = % 25 . 10 1 1 1025 . 1 Rate Year 2 = = 1025 . 0 1 ) 05 . 1 )( 05 . 1 ( + = 5 Finance - I (MGCR 341) – Prof. de Mot a Adjusting the Discount Rate to Different Periods % 02 . 44 1 1) 0.00 (1 Rate Discount nnual Equivalent 365 = + = A 1 r) (1 Rate Discount Period - Equivalent n + = n % 54 . 9 1 0.2) (1 Rate Discount nnual Equivalent 0.5 = + = A Example 1. Quoted Rate: 0.1% per day 2. Quoted Rate: 20% per a two-year period % 31 . 2 1 0.2) (1 Rate Discount Quarterly Equivalent 8 1 = + = 6 Finance - I (MGCR 341) – Prof. de Mot a If a bank pays 24% over a six-year period, what is the effective annual rate? a. 3.65% b. 4.00% c. 90.66%

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2 7 Finance - I (MGCR 341) – Prof. de Mot a If a bank pays 24% over a six-year period, what is the effective annual rate? % 65 . 3 1 0.24) (1 Rate Anual Equivalent 6 1 = + = 8 Finance - I (MGCR 341) – Prof. de Mot a Problem Your bank account pays interests monthly with an effective annual rate of 6%. Part a. What interest rate will you earn each month? % 4868 . 0 1 0.06) (1 Rate onthly Equivalent 12 1 = + = M 9 Finance - I (MGCR 341) – Prof. de Mot a Problem (cont) Part b. If you have no money in the bank now, how much will you need to save at the end of each month to accumulate \$100,000 in 10 years? The proposed cash flow stream is a 120 period annuity (i.e., 10 years x 12 months) with and interest rate of 0,4868% per period (i.e., per month) and a future value of \$100,000. The problem asks for the constant payment C of this annuity. Using the future value of annuity formula and solving for C: [] month per 47 . 615 \$ 1 ) 004868 . 0 1 ( 004868 . 0 1 000 , 100 1 ) 1 ( 1 120 = + = + = n n r r FV C 10 Finance - I (MGCR 341) – Prof. de Mot a What is the present value on a lottery prize that is to be received in 40 equal semi-annual payments of \$125,000, with the first payment beginning in one year ? Assume an EAR of 7%. a. 1,666,463 b. 2,604,454 c. 2,694,047 11 Finance - I (MGCR 341) – Prof. de Mot a What is the present value on a lottery prize that is to be received in 40 equal semi-annual payments of \$125,000, with the first payment beginning in one year? Assume an EAR of 7%. Solution Effective Six-Month Rate () 3.44% 1 07 . 0 1 5 . 0 = + = 454 , 604 , 2 ) 0344 . 0 1 ( 1 1 0344 . 0 000 , 125 0344 . 0 1 1 40 = + + = PV 12 Finance - I (MGCR 341) – Prof. de Mot a Annual Percentage Rate (APR) Annual Percentage Rate (APR): The rate that you would receive over one year if your investment earned a simple interest rather than compounded interest.
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Lecture 3 - Interest Rates - Required Reading INTEREST...

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