______
Name
CALCULATING INTEREST
Read the information below about calculating interest. Then complete the activities as directed. Compare your answers with those of a classmate.
Calculating Simple Interest
Simple interest is calculated using the following formula:
Interest = Principal x Rate x Time (I = PRT)
Interest (I) is the amount of interest expressed in dollars and cents.
Principal (P) is the amount of money earning interest.
Rate (R) is the annual percentage rate expressed as a decimal or fraction.
Time (T) is the length of time expressed in years.
Example: Find the simple interest on a $675 deposit for six months at 4%.
I=PRT
I=$600x.04x0.5
I=$12
1.Find the simple interest on a $5,250 deposit for 9 months at 3.5%.
2.Find the simple interest on a $2,550 deposit for 18 months at 5%.
3.Find the simple interest on a $3,500 deposit for 3 months at 4.75%.
Calculating Compound Interest
Interest can be compounded for different periods. Commonly used interest periods are daily, monthly, quarterly, and semiannually. The interest for any period is calculated on the compounded amount. The compounded amount is the total amount of money at the beginning of the next interest period, assuming that no deposits or withdrawals will be made. Because calculating compound interest for an extended period of time can be time-consuming, banks use compound interest tables to find the compounded amount.
To gain an understanding of compound interest, in this activity, you will compute compound interest for a short period.
Example: Find the interest and compound amount at the beginning of the fourth quarter on an $800 deposit that earns 6% interest compounded quarterly after 9 months. Assume that no deposits or withdrawals were made.
Beginning of second quarter:
I=P (Compound Amount)RT
I=$1,100x0.06x0.25
I=$16.50
Compound Amount at beginning of second quarter = Compound Amount at beginning of first quarter + Interest earned for the first quarter
Compound Amount at beginning of second quarter = $1,000 + $16.50
Compound Amount at beginning of second quarter = $1,016.50
Interest earned at the beginning of the second quarter = $16.50
Beginning of third quarter:
I=P (Compound Amount)RT
I=$1,116.50x0.06x0.25
I=$16.75
Compound Amount at beginning of third quarter = Compound Amount at beginning of second quarter + Interest earned for the second quarter
Compound Amount at beginning of third quarter = $1,116.50 + $16.75
Compound Amount at beginning of third quarter = $1,133.25
Interest earned at the beginning of the third quarter = $16.50 + $16.75 = $33.25
Beginning of fourth quarter:
I=P (Compound Amount)RT
I=$1,133.25x0.06x0.25
I=$17
Compound Amount at beginning of fourth quarter = Compound Amount at beginning of third quarter + Interest earned for the third quarter
1.Find the interest and compound amount for the beginning of the third quarter on a $5,000 deposit that earns 4% interest compounded quarterly after 6 months. Assume that no deposits or withdrawals were made.
2.Find the interest and compound amount for the beginning of the third quarter on a $20,000 deposit that earns 5% interest compounded quarterly after 9 months. Assume that no deposits or withdrawals were made.
Comparing Compound Interest and Simple Interest
1.If the $20,000 deposit at 5% interest for 9 months was calculated using simple interest, how much interest would be earned?
2.If you compare the interest earned in problem 2 under Compound Interest with that earned in problem 1 above, how much interest will have been earned through compounding?