Notes: September 1, 2011- Model for Accumulation

Today in class we continued out discussion from Wednesday about accumulating. Wednesday we learned about the geometric series, which is used to calculate how much one can accumulate by depositing uniform amounts of money at a fixed rate over a fixed period of time.






ex: You are thinking of starting a savings account to save up for a new car by the time that you graduate from college. (Your about to be a freshman in college). You get an awesome deal with the bank, you deposit $100 dollars every month at a rate of 10% compounded monthly. How much do you have to spend on a car by the end of college? (assuming its a four year degree)

A= 100[( (1+.00834)^48 -1)/ (.00834)]= $5872.24




We also specified when you should use the old ways of finding the effective rate and when to use the new way (the new formula): Which one you use is dictated by how much information that you have-

When you are given: the principle, and the new balance use the old method
new value - old value/ old value
When you are given: the nominal rate (rate advertised) and the compounding interval
A=d[ (1+i)^n - 1/ i]
The two formulas can be used together in order to solve other types of problems as well. Say that you are given the principle, and the new balance, and then asked to find the nominal rate:

1) find the effective rate using new-old/old
2) plug the value of the effective rate you just found into "A" in the new formula, then plug in all other known values and solve algebraically. Keep in mind that you may have to use the reciprocal of the exponent, n (taking the nth root of both sides)