Simple And Compound Interest
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Simple and Compound Interest
Quick Question
"What are some ways to take care of hard-earned money?" 2
Definition of Terms ▰ Lender
or creditor - person (or institution) who invests the money or makes the funds available ▰ Borrower or debtor - person (or institution) who owes the money or avails of the funds from the lender ▰ Origin or loan date - date on which money is received by the borrower
3
Definition of Terms ▰ Repayment date or maturity date - a date on which the
money borrowed or loan is to be completely repaid ▰ Time or term (t) - amount of time in years the money is borrowed or invested; length of time between the origin and maturity dates ▰ Principal (P) - amount of money borrowed or invested on the origin date 4
Definition of Terms ▰ Rate
(r) - annual rate, usually in percent, charged by the lender, or rate of increase of the investment ▰ Interest (I) - amount paid or earned for the use of money ▰ Simple Interest (Is) - interest that is computed on the principal and then added to it 5
Definition of Terms ▰ Compound
Interest (Ic) - interest is computed on the principal and also on the accumulated past interests ▰ Maturity value or future value (F) - amount after t years; that the lender receives from the borrower on the maturity date
6
Example 1 ▰
“Suppose you won 10,000 pesos and you plan to invest it for 5 years. A cooperative group offers 2% simple interest rate per year. A bank offers 2% compounded annually.
7
Solution (Simple Interest) Time (t)
1 2 3 4 5
Principal (P)
10,000
Interest Rate (r)
Simple Interest Solution
Answer
Amount after t years (Maturity Value)
2% 2% 2% 2%
(10000)(0.02)(1)
200
10,000 + 200 = 10,200.00
(10000)(0.02)(2)
400
10,000 + 400 = 10,400.00
(10000)(0.02)(3)
600
10,000 + 600 = 10,200.00
(10000)(0.02)(4)
800
10,000 + 800 = 10,800.00
2%
(10000)(0.02)(5)
1,000
10,000 + 1,000 = 11,000.00 8
Solution (Compound Interest) Compound Interest
Time (t)
Principal (P)
Interest Rate (r)
Solution
Answer
Amount after t years (Maturity Value)
1
10,000
2%
(10000)(0.02)(1)
200
10,000 + 200 = 10,200.00
2
10,200
2%
(10,200)(0.02)(1)
204
10,200 + 204 = 10,404.00
3
10,404
2%
(10,400)(0.02)(1)
208.08
10,404 + 208.08 = 10,612.08
4
10,612.08
2%
(10, 612.08)(0.02)(1)
212.24
10,612.08 + 212.24 = 10,824.32
5
10,824.32
2%
(10,824.32)(0.02)(1)
216.49
10,824.32 + 216.49 = 11,040.81 9
“
Among the two solutions presented, which will you choose and why?” 10
“
Now, let us compare the accumulated interest of the 2 investment after 5 years”
11
Final Intersets
Simple Interest (in pesos): 11,000 - 10,000 = 1,000 ▰ Compound Interest (in pesos): 11,040.81 - 10,000 = 1,040.81 ▰
12
Comparing the 2 “ tables, what have you observed?” 13
THANKS! 14
Quick Question
"What are some ways to take care of hard-earned money?" 2
Definition of Terms ▰ Lender
or creditor - person (or institution) who invests the money or makes the funds available ▰ Borrower or debtor - person (or institution) who owes the money or avails of the funds from the lender ▰ Origin or loan date - date on which money is received by the borrower
3
Definition of Terms ▰ Repayment date or maturity date - a date on which the
money borrowed or loan is to be completely repaid ▰ Time or term (t) - amount of time in years the money is borrowed or invested; length of time between the origin and maturity dates ▰ Principal (P) - amount of money borrowed or invested on the origin date 4
Definition of Terms ▰ Rate
(r) - annual rate, usually in percent, charged by the lender, or rate of increase of the investment ▰ Interest (I) - amount paid or earned for the use of money ▰ Simple Interest (Is) - interest that is computed on the principal and then added to it 5
Definition of Terms ▰ Compound
Interest (Ic) - interest is computed on the principal and also on the accumulated past interests ▰ Maturity value or future value (F) - amount after t years; that the lender receives from the borrower on the maturity date
6
Example 1 ▰
“Suppose you won 10,000 pesos and you plan to invest it for 5 years. A cooperative group offers 2% simple interest rate per year. A bank offers 2% compounded annually.
7
Solution (Simple Interest) Time (t)
1 2 3 4 5
Principal (P)
10,000
Interest Rate (r)
Simple Interest Solution
Answer
Amount after t years (Maturity Value)
2% 2% 2% 2%
(10000)(0.02)(1)
200
10,000 + 200 = 10,200.00
(10000)(0.02)(2)
400
10,000 + 400 = 10,400.00
(10000)(0.02)(3)
600
10,000 + 600 = 10,200.00
(10000)(0.02)(4)
800
10,000 + 800 = 10,800.00
2%
(10000)(0.02)(5)
1,000
10,000 + 1,000 = 11,000.00 8
Solution (Compound Interest) Compound Interest
Time (t)
Principal (P)
Interest Rate (r)
Solution
Answer
Amount after t years (Maturity Value)
1
10,000
2%
(10000)(0.02)(1)
200
10,000 + 200 = 10,200.00
2
10,200
2%
(10,200)(0.02)(1)
204
10,200 + 204 = 10,404.00
3
10,404
2%
(10,400)(0.02)(1)
208.08
10,404 + 208.08 = 10,612.08
4
10,612.08
2%
(10, 612.08)(0.02)(1)
212.24
10,612.08 + 212.24 = 10,824.32
5
10,824.32
2%
(10,824.32)(0.02)(1)
216.49
10,824.32 + 216.49 = 11,040.81 9
“
Among the two solutions presented, which will you choose and why?” 10
“
Now, let us compare the accumulated interest of the 2 investment after 5 years”
11
Final Intersets
Simple Interest (in pesos): 11,000 - 10,000 = 1,000 ▰ Compound Interest (in pesos): 11,040.81 - 10,000 = 1,040.81 ▰
12
Comparing the 2 “ tables, what have you observed?” 13
THANKS! 14
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