FORMULAS Effective interest rate compounded continuously ei 1 100 Annuity due PV of ordinary annuity interest rate X PV of ordinary annuity X PV of annuity due What is the present value on the same set of payments if they occurred at the BEGINNING of the year PV 1 interest rate Amortized Loan interest is paid off first Perpetuity Payment IRR Compounded continuously years I Y ex money Choice A Receive 20 000 today Choice B Receive 21 000 one year from now If your opportunity cost of money discount rate is 15 which choice will you accept Choice A you can invest in a bank that offers 5 daily compounding of interest Choice B you can invest in another bank offering you 5 continuous compounding Which choice will you pick FV 21 000 PICK OPTION A I 15 N 1 CPT PV 18260 Choice A ICONV NOM 5 C Y 365 CPT EFF 5 126 Choice B ex 0 05 1 100 5 127 PICK CHOICE B Assume a preferred stock pays you a dividend of 5 55 per year forever If your required rate of return is 6 66 how much is this preferred stock worth today 5 55 0666 83 The present value of a series of payments that occur at the end of each year 10 000 What is the present value of the same set of payments if the payments occurred at the beginning of each year The interest rate that applies to the problem is 8 8 no other data is needed to answer the question 10 000 1 0 088 10 880 Offer A Someone will give you 10 000 fifteen years from now Offer B Someone will give you 7 000 fourteen years from now and an additional 3 000 sixteen years from now Your discount rate is 7 7 Which is the better deal for you Offer A Find PV of lump sum of 10 000 3 286 7 Offer B find PV of the two lump sums and add them up 3393 So pick offer B as it is higher You invest 23 000 in a bank that pays 9 compounded continuously How much will you accumulate at the end of 12 years in this account 12 09 ex 23 000 67 727 An investment is available to you that pays you 100 per year forever If your required rate of return is 16 what is the most you will pay for this investment 100 0 16 625