Today's lesson, which wraps up our "once-through" of the most common concepts on a high school test, is probably the most practical lesson to understand. My education is in personal finance, and it baffles me how many people do not grasp the concept of compounding interest. One of my favorite quotes (by an unknown author) goes something like this: "He who understands the idea of compound interest earns it, while he who doesn't understand it pays it.
This concept appeared 10 times on last year's tests, always at question # 80.
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The biggest key to getting these questions right is to know the difference between simple interest and compound interest:
- Simple interest is interest earned only on the principal (the original amount invested)
- Compound interest is interest earned on the principal and interest.
Since simple interest should be simple, let's start there.
How to Calculate Simple Interest:
Use the formula I = Prt, where:
- P = the principal (original amount) invested
- r = the rate of interest the investment earns
- t = the time invested
One way to reduce errors is to remove the % sign while removing 2 zeros from the principal amount.
Example 1: * The interest on $5000 for 2.5 years at a simple interest rate of 1.5% is ___ dollars (integer)
- I = Prt = ($5000)(1.5%)(2.5)
- I = (50)(1.5)(2.5) = 50 x 3.75 = 187.50
- Since the answer has to be an integer, write 187.
Example 2: * The simple interest on $4,500.00 at 4.5% for 4.5 years is ___ dollars (integer)
- I = Prt = ($4500)(4.5%)(4.5)
- I = (45)(4.5)(4.5) = 45 x 20.25
- Round 20.25 down to 20. 45 x 20 = 900
- The exact answer is $911.25, and the acceptable (+/- 5%) range is from 866 to 956.
Example 3: * The simple interest on $1250 at 2.5% for 3.75 years is ___ dollars (integer)
- I = Prt = ($1250)(2.5%)(3.75)
- I = (12.5)(2.5)(3.75)
- Use Mult125var to multiply 3.75 x 12.5: 3.75 x 1/8 x 100 = .46875 x 100 = 46.875
- We are left with 2.5 x 46.875, so change it to 2.5 x 47. Use Mult25: 47 x 1/4 x 10 = 11.75 x 10 = 117.5
- Since the answer has to be an integer, write 117.
- The exact answer is $117.1875, and the acceptable (+/- 5%) range is from 112 to 123.
How to Calculate Compound Interest:
Example 4: * The compound interest on $3000 for 2 years at 6% compounded annually is ___ dollars (integer)
Example 5: * The compound interest on $2000 for 4 years at 8% compounded annually is ___ dollars (integer)
Example 6: * The interest on $2000 for 4 years at 6% compounded semiannually is ___ dollars (integer)