Dr. H. H. Friedman
Review of Mathematics of Finance--Corporation Finance

(1) You currently have $2,000.  How much will you have at the end of 6 years at 10% interest if interest is: (a) compounded annually? [$3543.12] (b) compounded quarterly? [$3617.45]  (c) compounded monthly?  [$3635.19]  (d) compounded daily?  [$3643.94]  (e) compounded continuously?  [$3644.24]

(2)  You currently have $6,000.   How much will you have at the end of 8 years at 4% interest if interest is: (a) compounded annually? [$8211.41] (b) compounded quarterly? [$8249.64]  (c) compounded monthly?  [$8258.37]  (d) compounded daily?  [$8262.62]  (e) compounded continuously?  [$8262.77]

(3)  How long will it take for money to triple at: (a) 10% interest?  [11.53 years ] (b) 8% interest?  [14.27 years]  (c) 6% interest?  [18.85 years]

(4)  How long will it take for money to quadruple at: (a) 9% interest?  [16.09 years ] (b) 7% interest?  [20.49 years]  (c) 5% interest?  [28.41 years]

(5)  A country has a population growth rate of 3.5%.  The population of this country will double in ___ years [20.15]

(6)  You buy a zero-coupon bond with a $5,000 face value and 20 years to maturity.  You paid $2000.  Calculate the implicit interest rate.  [4.69%]

(7)  You buy a zero-coupon bond with a $10,000 face value and 10 years to maturity.  You paid $5000.  Calculate the implicit interest rate.  [7.18%]

(8)  You borrow  $100,000 and must repay $220,000 at the end of 12 years.  Calculate the implicit interest rate.  [6.79%]

(9)  You set aside $4,000 yearly and interest rates are 7%.  How much will you have at the end of 50 years? [$1,626,115.72]

(10)  You set aside $2500 yearly and interest rates are 5%.  How much will you have at the end of 40 years [$302,000]

(11)  A firm wants to retire $250,000,000 in bonds in 30 years.  How much should they set aside today if they can earn 11%? [$10,920,704.23]

(12)  You would like to have $500,000 at the end of 20 years to buy a retirement home. The interest rate is 7%. (a) How much should you set aside today?   [$129,209.50]  (b)  How much should you set aside yearly? [$12,196.46]

(13)  You would like to have $300,000 at the end of 20 years to buy a nice present for Professor Friedman. The interest rate is 5%. (a) How much should you set aside today?   [$113,066.84]  (b)  How much should you set aside yearly? [$9072.76]

(14)  What is the value (today) of an annuity that will pay you at age 60,  $8,000 per year for twenty years and interest rates are 7%?  You are thirty years old.  [$11,136.41]

(15)  What is the value (today) of an annuity that will pay you at age 70,  $20,000 per year for twenty years and interest rates are 6%?  You are twenty years old.  [$12,456.31]

(16)  You borrow $5,000 and must repay $1,000 per year (at the end of the year) for the next 8 years.  Find the implicit interest rate.  [about 12%]

(17)  You borrow $5,000 and must repay $1,000 per year (at the end of the year) for the next 10 years.  Find the implicit interest rate.  [about 15%]

(18)  You borrow $14,000 and must repay $2,000 per year (at the end of the year) for the next 10 years.  Find the implicit interest rate.  [about 7%]

(19)  You borrow $50,000 and must repay $10,000 per year (at the end of the year) for the next 11 years.  Find the implicit interest rate. [about 16%]

(20)  IBM bond with a $1,000 face value, an   8% coupon, and 15 years to maturity; interest is paid semi-annually.  What is the value of the bond if the market rate of interest (desired yield to maturity) is 10%?   [$846.30]

(21)  INTEL bond with a $1,000 face value, a 10% coupon, and 20 years to maturity; interest is paid semi-annually.  What is the value of the bond if the market rate of interest (desired yield to maturity) is 6%?   [$1462.34]

(22)    SPRINT bond with a $1,000 face value, a 12% coupon, and 10 years to maturity; interest is paid semi-annually.   What is the value of the bond if the market rate of interest (desired yield to maturity) is 8%?  [$1271.82]

(20)  ATT bond with a $1,000 face value, a   7% coupon, and 25 years to maturity; interest is paid semi-annually.  What is the value of the bond if the market rate of interest (desired yield to maturity) is 10%?   [$726.16]

(21)  ATT bond with a $1,000 face value, a 4% coupon, and 15 years to maturity; interest is paid semi-annually.  If the price is $804, what is the desired yield to maturity (market rate of interest)?  Hint:   Solve using trial and error. [6%]

(22)  IBM bond with a $1,000 face value, a 7% coupon, and 25 years to maturity; interest is paid annually.  If the price is $804, what is the desired yield to maturity (market rate of interest)?  [9%]

(22)  INTEL bond with a $1,000 face value, a 10% coupon, and 20 years to maturity; interest is paid annually.  If the price is $1459, what is the desired yield to maturity (market rate of interest)?  [6%]

(23)  (a) Microsoft bond with a $1,000 face value, a 14% coupon, and 15 years to maturity; interest is paid annually.  If the price is $1304, what is the desired yield to maturity (maket rate of interest)?   [10%]
(b) HP bond with a $1000 face value, a 10% coupon, and 30 years to maturity.  If the price is $839, what is the desired yield to maturity (market rate of interest)?   [12%]

(24)  You currently have $20,000.  How much will you have at the end of 5 years at 12% interest if interest is: (a) compounded annually? [$35,246.83] (b) compounded quarterly? [$36,122.22]  (c) compounded monthly?  [$36,333.93]  (d) compounded daily?  [$36438.78]  (e) compounded continuously?  [$36442.38]