1. ## Annuity problem

You can purchase a residential building lot for $60,000 cash, or for$10,000 down and month-end payments of $1000 for five years. If money is worth 7.5% compounded monthly, which option should you choose? Answer: Second option is$94.69 cheaper

2. ## Annuity

The value of the annuity is X * (1-v^n)/i' where

i = 7.5%
i' = 7.5%/12 = 0.625% i.e. the monthly interest rate
v = (1+i')^-1 = 0.99378882
X = 1000
n = 5 * 12 = 60

Annuity = 1000 * ( 1- 0.99378882^60) / 0.00625 = 49905.31

Adding the 10000 downpayment gives 59905.31 i.e. a saving of 94.69