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### Grade 8 - Mathematics9.18 Compound Interest - I

Simple interest is calculated on the original principal only. Accumulated interest from prior periods is not used in calculations for the following periods. It is normally used for a single period of less than a year, such as 30 or 60 days.

Compound interest is calculated each period on the original principal and all interest accumulated during past periods. Although the interest may be stated as a yearly rate, the compounding periods can be yearly, semiannually, quarterly, or even continuously.

Compound interest can be thought of as a series of back-to-back simple interest contracts. The interest earned in each period is added to the principal of the previous period to become the principal for the next period.

Example
Find the value of a \$1000 savings account after 4 and half years if the account pays 6% interest compounded semiannually.
Solution:
6% interest compounded semiannually means that the interest is paid twice a year or every 6 months. The interest rate is 6% divided by 2 that is 3%.
Rate = 0.03 (The rate is entered as decimal)
The interest is added to the principal every 6 months.
 Principal Interest New Interest Time (year) 1000.00 30.00 1030.00 0.5 1030.00 30.90 1060.90 1 1060.90 31.83 1092.73 1.5 1092.73 32.78 1125.51 2.0 1125.51 33.77 1159.28 2.5 1159.28 34.78 1194.06 3.0 1194.06 35.82 1229.88 3.5 1229.88 36.90 1266.78 4 1266.78 38.00 1304.78 4.5
The value of the savings account after 4 and half years is \$1304.78.
Directions: Solve the following problems. Also write at least 5 examples of your own.
 Q 1: Find the amount at compound interest on \$76200 for 2years at 5%.\$84050.5\$84010.5\$84030.5\$84020.5 Q 2: Find the amount at compound interest on \$7600 for 2years at 3%.\$8062.84\$8650.84\$8060.84\$8064.84 Q 3: Find the amount at compound interest on \$4,600 for 3years at 6%.\$5,375.67\$5,475.67\$5,478.67\$5,380.67 Q 4: Find the amount at compound interest on \$21600 for 2years at 5%.\$23850\$23814\$23840\$23841 Q 5: Find the amount at compound interest on \$6100 for 2years at 5%.\$6750.75\$6725.25\$6750.25\$6725.75 Q 6: Find the amount at compound interest on \$15000 for 3years at 8%.\$18850.68\$18890.68\$18985.68\$18895.68 Q 7: Find the amount at compound interest on \$6500 for 3years at 6%.\$7740.60\$7750.60\$7751.60\$7741.60 Q 8: Find the amount at compound interest on \$26100 for 3years at 2%.\$27597.53\$27590.53\$27697.53\$27690.53 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!

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