ELLA AND THELMA EACH INVEST PHP10,000 FOR TWO YEARS, BUT
UNDER DIFFERENT SCHEMES. ELLA EARNS 2% OF PHP10,000 THE
FIRST YEAR, WHICH IS PHP200, THEN ANOTHER PHP200 THE
SECOND YEAR. THELMA EARNS 2% OF PHP10,000 THE FIRST YEAR,
WHICH IS PHP200, SAME AS ELLA’S. BUT DURING THE SECOND
YEAR, SHE EARNS 2% OF THE PHP10,000 AND 2% OF THE PHP200
ALSO.
ELLA – PHP 10,400
THELMA – PHP 10,404
COMPOUND INTEREST
WHEN THE INTEREST DUE AT THE END OF A CERTAIN PERIOD
IS ADDED TO THE PRINCIPAL AND THAT THE SUM EARNS
INTEREST FOR THE NEXT PERIOD, THE INTEREST PAID IS
CALLED COMPOUND INTEREST.
EXAMPLE
PHP 40,000.00 WAS LOANED FOR A PERIOD OF 3
YEARS WITH 6% INTEREST COMPOUNDED ANNUALLY.
THE TABLE SHOWS THE AMOUNT DUE AT THE END OF
EACH YEAR.
Principal at the
start of the year
Interest
First Year
PHP 40,000.00
40,000(0.06)(1)
=PHP 2,400.00
Second Year
PHP 42,400.00
42,400(0.06)(1)
=PHP 2,544.00
Third Year
PHP 44,944.00
44,944.00(0.06)(1)
=PHP 2,696.64
Amount at the end
of the year
PHP40,000+PHP
2,400
=PHP 42,400.00
PHP 42,400+PHP
2,544
=PHP 44,944.00
PHP44,944.00+PHP
2,696.64
=PHP 47,640.64
THE AMOUNT (A) AT THE END OF THE YEAR IS EQUAL TO THE SUM OF THE
PRINCIPAL (P) AND THE INTEREST (PR) FOR THAT YEAR. IN SYMBOLS,
F = P + PR = P(1+R)
THUS,
FIRST YEAR:
A=40,000(1+0.06)
= PHP 42,400.00
SECOND YEAR:
A=42,400(1+0.06)
=40,000(1+0.06)(1+0.06)
=40,000(1 + 0.06)2
= PHP 44,944.00
THIRD YEAR:
A=44,944(1+0.06)
=40,000(1 + 0.06)2 1 + 0.06
=40,000(1 + 0.06)3
= PHP 47,640.60
IN GENERAL, WHEN INTEREST IS COMPOUNDED ANNUALLY FOR N YEARS, THE AMOUNT
(MATURITY OR FUTURE VALUE), A, IS GIVEN BY THE FORMULA
F = P (𝟏 + 𝒓)𝒕
THE COMPOUND INTEREST, 𝐼𝑐 , IS GIVEN BY THE FORMULA
𝑰𝒄 = F-P
NOTE: BECAUSE INTEREST IS PAID ON INTEREST, COMPOUND INTEREST IS ALWAYS
GREATER THAN SIMPLE INTEREST.
PRESENT VALUE
𝑨
𝑷=
𝟏+𝒓
𝒕