LESSON 3_MATHEMATICS OF FINANCE (Mathematics)

Mathematics of Finance

1. LESSON 3: MATHEMATICS OF FINANCE SIMPLE AND COMPOUND INTEREST

2. Definition of Terms simple and compound interest Lender or creditor – person or institution who invest the money or makes the funds available Borrower or debtor - 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 Repayment date or maturity date - on the which the money borrowed or loan is to be completely repaid

3. Definition of Terms simple and compound interest Time or term (t )- amount of time in years the money is borrowed or invested; length of time between origin and maturity dates Principal ( P)- amount of money borrowed or invested on the origin date Rate (r) annual rate, usually in percent , charged by the lender, 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.

4. Definition of Terms simple and compound interest Compound Interest ( Ic ) interest is computed on the principal and also on the accumulated past interest Maturity value or future value (F)- amount after t years; that the lender receives from the borrower on the maturity date.

5. Simple Interest

6. SIMPLE INTEREST -defined as I= Prt Where, I= interest earned per year P= original amount (invested, loan, deposited, et.al) r= rate of interest (expressed in decimal) t= time (per year)

7. Example 1 A bank offers 0.25 % annual simple interest rate for a particular deposit . How much interest will be earned If 1,000, 000.00 peso is deposited in this in this saving account for 1 year

8. Example 2 How much interest is charged when P50,000.00 is borrowed for 9 months at annual simple interest rate of 10 %. I P r t

9. Example 3 When invested at an annual interest rate of 7%, an amount earned P 11,200 of simple interest in two years. How much was originally invested? I P r t

10. Example 4 If an entrepreneur applies for a loan amounting to P500,000.00 in a bank, the simple interest of which is P157,500 for 3 years, what interest rate is being charged?

11. Exact & Ordinary Interest Exact Interest is computed in a 365 days in a year as the time factor denominator. t = Number of Days of a Loan/365 I= Prd /365 Ordinary interest is a type of interest wherein the number of days is computed based on 360 days in a year. t = Number of Days of a Loan/360 I= Prd /360

12. Approximate & Actual Time Approximate time uses 30 days in every month, while the actual time uses the exact number of days in every specific month.

13. Example: Find the interest on Php 28,700 from March 14, 2014 to August 16, 2014 at 10% simple interest rate using the following: a. Ordinary Interest using actual time b. ordinary interest using approximate time c. exact Interest using actual time d. exact interest using approximate time

14. Example: Find the exact interest on Php 208,700 from February 14, 2012 to December 30, 2012 at 10.5% simple interest rate. Ans: Php 19,159.34

15. Maturity Value Many person or institution are interested to know the amount that a lender will give to the borrower on the maturity date. For instance, you may be interested to know the total amount of money in a savings account after (t) years at an interest rate ( r) this amount is called the maturity value or future value (F)

16. Maturity ( future )Value Where F= P+I F= maturity ( future) value P= principal I = simple interest

17. Subtituting Is by Prt gives F= P + Prt F= P( 1+rt ) Where F= maturity value P= principal r= interest t=term/ time in years

18. Maturity value Find the maturity value if 1 million is deposited in a bank at an annual simple interest rate of 0. 25 % & after 1 year and 5 years?

19. Activity 5 Principal Rate Time Interest Maturity Value F 60,000 4% 15 years (1) (2) (3) 12% 5 months 15,000 (4) 50,000 (5) 2 years (6) 59,500 (7) 10.5% (8) 157,500 457,500 1,000,000 0.25% 6.5 months (9) (10)

20. Compound Interest COMPOUND INTEREST -defined as Where, F=Maturity/final amount (principal +interest) P= principal (original amount) r= rate of interest n= number of compounding periods per year t= time (length of time in years)  

21. Compounding Frequencies and Periods Compounding or Conversion Frequency No. of Compounding or conversions per year Compounding or conversion periods Annual 1 1 year Semi-annual 2 6 months Quarterly 4 3 months Bimonthly 6 2 months Monthly 12 1 month

22. Example 1 Find the maturity value and the compound interest if P 10, 000.00 is compounded annually at interest rate of 2% in 5 years.

23. Example 2 Find the maturity value and interest if 50,000 is invested at 5% compounded monthly for 8 years.

24. Example 3 Mrs. Sirug wants to provide a P200,000 graduation gift for her daughter Sofia. She is now 16 years old, and she would like the fund to be available by the time she is 20. She decides on an investment that pays 10% compounded quarterly. How large must the deposit be?

25. Activity 6 What will be the maturity value of P12,000 invested for 4 years at 15% compounded quartery ? What amount must be invested now in savings account earning 9% compounded semi-annually to accumulate a total of 21,000 after 4 ¾ years?