You just learned that your grandmother left you a perpetuity…

You just learned that your grandmother left you a perpetuity in her will that was intended to pay you $1,000 per year for the rest of your life.  Grandma anticipated that you would make 8%, but you have only managed to average 5%. How much more should Grandma have deposited in the account?  

Eight years ago, you took out a mortgage on your home and ar…

Eight years ago, you took out a mortgage on your home and are currently considering refinancing into a loan at a lower rate and for a shorter term.  Your original loan was for 30 years, at 4.5% interest on the $200,000 borrowed, and you pay monthly.  The new loan you are considering will be for 15 years at a rate of 2.5%.  Again, the payments will be monthly.  What will your new payment be if you take on this new loan? (hint: first, find the balance remaining)