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A math activity sheet from the Balagtas National Agricultural High School in the Philippines, focusing on the topic of compounding interest when it is compounded more than once a year. objectives, procedures, examples, and activities for students to understand and apply the concepts of compounding interest, frequency of conversion, nominal rate, and maturity value. The students are expected to learn how to find the future value, present value, and interest rate when compounding more than once a year.
Typology: Quizzes
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Republic of the Philippines Department of Education Region III Schools Division Office of Bulacan Balagtas National Agricultural High School Pulong Gubat, Balagtas, Bulacan
A. Content Standards The learners demonstrate an understanding of key concepts of simple and compound interests. B. Performance Standards: The learner can investigate, analyze, and solve problems involving simple and compound interests. C. MELCs: a. computes interest, maturity value, future value, and present value in simple interest and compound interest environment. (M11GM-IIa-b-1) b. solves problems involving simple and compound interests. (M11GM- IIb-2) D. Specific Objectives:
Lesson 3: Compounding More Than Once A Year
A. Preliminary Activities
1. Pre-Test Multiple Choice: Read each question carefully, and then choose the letter of the correct answer that best fits the question below. (10 points)
Remember that in solving for the compound interest, the interest of the preceding year is added to the principal to the succeeding year and its is earning more interest compared to simple interest. This lesson will show you another method on how to earn interest better than the usual compound interest and that is compounding more than once a year.
But first, letโs define some new terms.
Maturity Value, Compounding m times a year
๐น๐น = ๐๐(1 + ๐๐)๐ก๐ก^ or ๐น๐น = ๐๐ (1 +
๐๐ ๐๐ ๐๐ )
๐๐๐ก๐ก
Where: F = maturity value P = principal j = ๐๐
๐๐ ๐๐ ; t = mt
im^ = nominal rate of interest (annual rate) m = frequency of conversion t = term/time in year
EXAMPLE 1. Find the maturity value and interest if Php 10,000 is deposited in a bank at 2 % compounded quarterly for 5 years.
Solution. Given: P = 10,000; i (4)^ = 0.02; t = 5 years; m = 4 Find: (a) F; (b) P Compute for the interest rate in a conversion period by
Compute for the total number of conversion periods given by
Compute for the maturity value using
Answer: The compound interest is given by
EXAMPLE 2. Find the maturity value and interest if Php 10,000 is deposited in a bank at 2 % compounded monthly for 5 years.
Solution. Given: P = 10,000; i (12)^ = 0.02; t = 5 years; m = 12 Find: (a) F; (b) P Compute for the interest rate in a conversion period by
Compute for the total number of conversion periods given by
Compute for the maturity value using
Answer: The compound interest is given by
and the total number of conversion periods is
The present value can be computed by substituting these values in the formula.
Thus,
Answer. The present value is P19,529.
EXAMPLE 1. How long will it take P3,000 to accumulate to P3,500 in a bank savings account at 0.25% compounded monthly?
Solution.
Given: P = 3,000; F = 3,500; i(12)^ = 0.0025; m = 12; j = ๐๐
( 12 ) 12 =^
Substituting the given values in the maturity value formula F = P(1 + j)n^ results to
To solve for n, take the logarithm of both sides.
Thus, payments should be made for 740 months or ๐ก๐ก = (^) ๐๐๐๐ = 74012 = 61.
years.
EXAMPLE 2. How long will it take P1,000 to earn P300 if the interest is 12% compounded semi-annually?
Solution.
Given: F = 1,300; m = 2; i (2)^ = 0.12; j = ๐๐
( 2 ) 2 =^
Because interest is earned only at the end of the period, then 5 six-month periods are needed so that the interest can reach P300. Thus, n = 5 and ๐ก๐ก = ๐๐ ๐๐ =^
5 2 = 2.5^ years. It will take 2.5 years for P1,000 to earn P300.
EXAMPLE 3. At what nominal rate compounded semi-annually wil P10, accumulate to P15,000 in 10 years?
Solution. Given: F = 15,000; P = 10,000; t = 10; m = 2; n = mt = (2)(10) = 20 Find: i(2)
The interest rate per conversion period is 2.05% The nominal rate (annual rate of interest) can be computed by
(Write your answers and solutions on a separate sheet.) A. Complete the table by computing the interest rate per period and the total number of conversion periods.
Nominal Rate i (m)
Interest compounded
Frequency of conversion (m)
Interest rate per conversion peiod 12% Semi-annually (1) (2) 16% Quarterly (3) (4) 9% Monthly (5) (6) 10.95% Daily (7) (8)
A. Solve the following problem.
B. Find the unknown.
