[size=12][font=Times New Roman]Tips for Doing Problems
When doing engineering economy problems, make sure:
"TIME FRAMES" MATCH:
If one period equals one quarter, then the interest rate should be quarterly and compounded quarterly. For example, if a yearly interest rate is given but interest is compounded monthly, divide the interest rate by 12.
ANSWER IS REASONABLE
ANSWER IS ROUNDED TO THE NEAREST PENNY
Sinking Fund
Definition: A sinking fund differs from compound interest in that we now have uniform payments over time in addition to the compound interest.
Sinking Fund Time Line
Example #1
Example: If you deposit $50 per month into an account that pays 6% interest, compounded monthly, for 2 years, how much is in the account immediately after the last deposit?
Please Note: Yearly interest in the equation is divided by 12 since payments are on a per-month basis.
Also Note: There are 24 payments, not 23 months.
Sinking Fund Time Line
Example #2
Example: Which is of more value to receive:
(a) $8000 today or
(b) 5 annual payments of $2000, beginning in 1 year?
(Assume 8% interest compounded annually.)
Sinking Fund Time Line
Example #3
Example: Which is of more value to receive:
(a) $8000 today or
(b) 5 annual payments of $2000, beginning in 1 year?
(c) 5 annual payments of $2000, beginning today?
(Assume 8% interest compounded annually.)
Annuity
NOTE: Follow the algebraic steps used to find the present value of a sinking fund. This is the formula for an annuity.
http://www.eng.iastate.edu/efmd/Captures/annline1.gifAPPLICATION: The first application of the annuity formula is to find the present value of a sinking fund. The second is using the formula in situations like the following example.
EXAMPLE: You borrow $5000 to buy a car. If you repay the loan with 36 monthly installments at 18% interest, what is the amount of each payment?
Summary
Compound InterestEquation: S = P (1 + I)^N
Sinking Fund