Understanding Simple Interest in Banking and Finance
Explore the concept of simple interest and its application in banking and finance. Learn how to calculate simple interest using the formula and solve examples to understand its practical implications. From earning interest on savings to owing interest on loans, grasp the fundamental principles of interest calculations effortlessly.
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Section 2.1 Simple Interest
Interest An important principle in banking and finance is the use of interest. Interest is simply when money is paid for the use of money. If you were to put money in a saving account, the bank would pay you interest in return for use of your money as investments.
Simple Interest A special type of interest called simple interest is used to compute the amount of money earned or owed on the balance of money known as the principle.
Simple Interest Formula Simple interest formula ? = ??? ? = ????????? ? = ???? ? = ????
Example 1 How much interest is earned if $600 is put in a savings account that pays 2% interest for 3 years?
Solution to Example 1 Use the simple interest formula. = 600 $ 00 . P = = 2 % 02 . I = 3 T years = = = = ($ 600 00 . )(. 02 ) 3 )( ($ 12 00 . ) 3 )( 36 $ 00 . I PRT
Example 2 You borrow $5000 from a bank that has an 8% interest rate for 4 years. How much simple interest do you owe the bank?
Solution to Example 2 Use the simple interest formula: = 5000 $ 00 . P = = 8 % 08 . I = 4 T years = = = = 5000 ($ 00 . )(. 08 ) 4 )( ($ 400 00 . ) 4 )( 1600 $ 00 . I PRT
Example 3 Complete the following on simple interest Interest Principal Rate Time $1,300.00 2.5 % 3 ????? a) ? b) $50 $ 600 3 % ? c) $120 $1200 ? 4 ?????
Solution to Example 3 Part a) Find the interest = 5 . 2 % 025 . , Convert then use the formula = I PRT = 1300 ($ )(. 025 ) 3 )( I = ($ 32 50 . ) 3 )( I = 97 $ 50 . I
Solution to Example 3 Part b) Find the time = 50 ( ) I $ PRT = Solve 03 )(. for T ($ 600 ) T = 50 $ 18 $ T 50 $ 18 $ T = 18 $ 18 $ = 7 . 2 years T
Solution to Example 3 Part c) Find the rate. = PRT I ( ) Solve for R = $ 120 ($ 1200 ) ) 4 ( R = $ 120 $ 4800 R $ 4800 R $ 120 = $ 4800 $ 4800 120 = R 4800 = = . 025 5 . 2 % R
Future Value When interest is computed in a saving account, it is then added to the balance or principle. This new balance or principle is known as the future value. Future Value Formula (Simple Interest) Future Value = Principle + Interest ? = ? + ? ? = ? + ??? ? = ? 1 + ??
Example 4 If $15,000 is deposited in a saving account earning 2.2 % simple interest, what is the future value in 5 years?
Solution to Example 4 Use the future value for simple interest formula = 15 $ 000 , = years P = 2 . 2 % 022 . R = 5 T = + ) 5 = + = = 15 $ 000 , 1 ( 022 . 15 $ 000 , 1 ( 11 . ) 15 $ 000 , . 1 ( 11 ) 16 $ 650 , A
Example 5 If $6,000 is deposited in a saving account earning 1.1 % simple interest, what is the future value in 5 years?
Solution to Example 5 Use the future value for simple interest formula = , 6 $ 000 P = = 1 . 1 = % years 011 . R 5 T = + ) 5 = + = = , 6 $ 000 1 ( 011 . , 6 $ 000 1 ( 055 . ) , 6 $ 000 . 1 ( 055 ) , 6 $ 330 00 . A
Example 6 (Finding the interest rate) If a business borrows $18,000 and repays $26,100 in 3 years, what is the simple interest rate?
Solution to Example 6 Use the future value formula = P = = 18 $ 000 , : 26 $ 100 , : 3 A T years = + 26 100 , 18 000 , 1 ( + 3 ) R = 26 100 , 18 000 , 54 000 , R = R + 26 100 , 18 000 , 18 000 , 18 000 , 54 000 , R = 8100 54 000 , 8100 54 000 , R = 54000 54 000 , or = = 15 . 15 % R R
Example 7 Suppose you wish to save $3,720. If you have $3000 and invest it at a 4% simple interest rate, how long will it take to obtain $3,720?
Solution to Example 7 Use the future value formula = , 3 $ 000 P = , 3 $ 720 = A = 4 % 04 . R = + , 3 720 , 3 000 1 ( + 04 . ) T = , 3 720 , 3 000 120 T = + , 3 720 , 3 000 , 3 = 000 , 3 000 120 T 720 120 T 720 120 T = 120 120 = 6 T years
Example 8 If $12,000 is deposited in a saving account earning 3 % simple interest, what is the future value in 5 years?
Solution to Example 8 Use the future value for simple interest formula = 12 $ 000 , = P = 3 % years 03 . R = 5 T = + ) 5 = + = = 12 $ 000 , 1 ( 03 . 12 $ 000 , 1 ( 15 . ) 12 $ 000 , . 1 ( 15 ) 13 $ 800 , A
