Compound Interest - More Than Once, Quarterly, Semi-Annually, Daily

mathematics

1. COMPOUND INTEREST Compounding More Than Once A Year September 2019

2. OBJECTIVES Illustrate compound interest more than once a year. Find the compound interest , maturity value , and present value when compounded more than once a year . 2

3. RECALL COMPOUND INTEREST 3 Compound interest is the interest computed from the _____________ plus the __________ accumulated from ___________ year/period.” principal interest previous

4. COMPOUND INTEREST RECALL When interest is compounded annually (yearly) , the MATURITY VALUE can be computed using  

5. COMPOUND INTEREST RECALL When interest is compounded annually (yearly) , the COMPOUND INTEREST can be computed using  

6. COMPOUND INTEREST RECALL When interest is compounded annually (yearly) , the PRESENT VALUE (principal) can be computed using  

7. How will you compute for the maturity value of a loan or investment if it is compounded MORE THAN ONCE a year? 7

8. 8 The 3 groups invested their P 100 on different banks compounding once a year, twice a year and 4 times a year. Which group has the greatest amount? What can you observe from the interest rate? What can you conclude from the table on compound interest?

9. MORE THAN ONCE A YEAR COMPOUND INTEREST When investment is compounded twice a year , the conversion period is 6 months and the frequency of conversion is 2 . Interest rate      

10. MORE THAN ONCE A YEAR COMPOUND INTEREST When investment is compounded quarterly , the conversion period is 3 months and the frequency of conversion is 4 . Interest rate      

11. 11 How many times did the interest is computed for 4 years? Group 1 = 4 times Group 2 = 8 times Group 3 = 16 times

12. MORE THAN ONCE A YEAR COMPOUND INTEREST When money is invested and computed with an interest that is compounded more than once a year, the number of conversion increases depending on the frequency of conversion in a year.

13. MORE THAN ONCE A YEAR COMPOUND INTEREST TERMS to REMEMBER: CONVERSION or INTEREST PERIOD – time between successive conversion of interest FREQUENCY OF CONVERSION (m) – number of conversion periods in a year NOMINAL RATE (r) – annual interest rate RATE PER CONVERSION PERIOD (j) – annual rate divided by the frequency of conversion TOTAL NUMBER OF CONVERION (n) – the product of frequency of conversion and the number of years  

14. LET’S TRY Conversion/ Interest Period One conversion period Semi-annually 6 months 2 Quarterly 3 months 4 Monthly 1 month 12 Daily 1 day 365 Conversion/ Interest Period One conversion period Semi-annually 6 months 2 Quarterly 3 months 4 Monthly 1 month 12 Daily 1 day 365 Frequency of conversion 2% annual rate

15. COMPOUNDING MORE THAN ONCE A YEAR MATURITY VALUE To compute for the maturity value of a loan/investment compounding YEARLY , we use the formula ….  

16. COMPOUNDING MORE THAN ONCE A YEAR MATURITY VALUE But since the interest is compounding more than once a year,       where j is the rate per conversion period and n is the total # of conversion

17. COMPOUNDING MORE THAN ONCE A YEAR MATURITY VALUE          

18. COMPOUNDING MORE THAN ONCE A YEAR COMPOUND INTEREST Use this equation to compute for the compound interest earned from an investment/loan that is compounded more than once a year.  

19. COMPOUNDING MORE THAN ONCE A YEAR COMPOUND INTEREST To identify the value of the principal or present value when the maturity value is given, use this equation.  

20. MORE THAN ONCE A YEAR COMPOUND INTEREST FOR EXAMPLE: Cris borrows Php 50, 000 and promise to pay the principal and interest at 12% compounded quarterly . How much must he pay after 6 years ?  

21. MORE THAN ONCE A YEAR COMPOUND INTEREST FOR EXAMPLE: Lito invested his Php 45, 000 earnings on a bank paying 18% compounded monthly interest. How much interest can he gain from his invested if he put the money in the bank for 5 years ?

22. MORE THAN ONCE A YEAR COMPOUND INTEREST FOR EXAMPLE: What is the present value of Php 50, 000 due in 4 years if the money invested at 12% compounded semi-annually ?

23. THANK YOU! Alexander Martensson Phone [phone] Email [email protected]

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