Problem No.
50
Alexander Michael owes P25,000 due in one year and P75,000 due in four years. He agrees to
pay P50,000 today and the balance in 2 years. How much must he pay at the end of two years if money is
worth 5% compounded semi-annually?
A. another P50,000 B. only P39,026.30 C. only P25,000 D. only P30,000.00
Given:
Po = P50,000
F1 = P25,000 @n = 1 year
F4 = P75,000 @n = 4 year
Semi-annualy = m = 2
Required:
the amount he must pay at the end of two years
Schematic Diagram:
Solution:
Using effective rate formula:
m
i n=( 1+i ) −1
2
0.05
(
i n= 1+
2 )
−1
i n=0.050625
And now using Compound Interest formula and using the solved effective rate;
F
P=
( 1+i )n
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P0 + P2=P1 + P4
F P 25,000 P75,000
P50,000+ = +
( 1+0.050625 ) ( 1+ 0.050625 ) ( 1+0.050625 )4
2 1
F=P39,021.27883
ANSWER: B
Discussion:
At first we need to get the effective rate using the given interest rate which is 5% compounded
semi-annually at given number of years which is 2 years and equate in terms of present worth using the
compound interest formula in the amount he owes and the amount he pays.
This study source was downloaded by 100000873674561 from CourseHero.com on 10-12-2023 07:18:13 GMT -05:00
https://www.coursehero.com/file/76372667/Problem-No-50docx/
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