13.7. Annuities for Loans http://www.ck12.org
13.7 Annuities for Loans
Here you’ll learn how to compute present values of equal periodic payments.
Many people buy houses they cannot afford. This causes major problems for both the banks and the people who
have their homes taken. In order to make wise choices when you buy a house, it is important to know how much you
can afford to pay each period and calculate a maximum loan amount.
Joanna knows she can afford to pay $12,000 a year for a house loan. Interest rates are 4.2% annually and most house
loans go for 30 years. What is the maximum loan she can afford? What will she end up paying after 30 years?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/57226http://www.youtube.com/watch?v=z1c34mW6FFs
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/57228http://www.youtube.com/watch?v=owzf31qZIA8
Guidance
The present value can be found from the future value using the regular compound growth formula:
PV( 1 +i)n=FV
PV=( 1 FV+i)nYou also know the future value of an annuity:
FV=R·(^1 +ii)n−^1
So by substitution, the formula for the present value of an annuity is:
PV=R·(^1 +ii)n−^1 ·( 1 +^1 i)n=R·(^1 i(+ 1 +i)ni)−n^1 =R·^1 −(^1 i+i)−n