SIM Gen Math 11 v2 - Compound Interest PDF

Preview

Summary

Compound Interest...

Description

STRATEGIC INTERVENTION MATERIALS GENERAL MATHEMATICS 11 Quarter 2

Solve problems involving Compound Interest

TITLE CARD

SOLVE PROBLEMS INVOLVING COMPOUND INTEREST M11GM-IIb-2 Objectives: 1. Solve problems that compute the Future Value. 2. Solve problems that compute the Present Value. 3. Solve problems that compute the Interest.

GUIDE CARD Compound interest is the procedure in which interest is periodically calculated and added to the principal. Conversion period (compounding period or interval period) is the time interval between succeeding interest calculations. The interest earned during a period is converted to principal at the end of the period because the principal and the interest combined and treated as the new principal for the succeeding period. The effect of converting interest to principal is that the interest earned in a period will also earn interest in all succeeding periods. The compound frequency (or conversion frequency ) is the number of compounding that take place in a year. Compounding Frequencies and Periods (Table 1.1) Compounding or No. of compounding or Compounding or conversion frequency conversions per year conversion periods Annual 1 1 year Semiannual 2 6 months Quarterly 4 3 months Bimonthly 6 2 months Monthly 12 1 month The nominal interest is the stated annual interest rate on which the compound interest calculation is based. The periodic interest rate is the rate of interest earned in one conversion period. F = Maturity value of the loan or investment P= Principal amount of the loan or investment I = Amount of interest paid or received J= Nominal interest rate m= Number of conversion per year t= Time period (term) of the loan or investment i = Periodic interest rate n=number of conversions of the loan The periodic interest rate I is computed using the formula 𝒋 𝒊=𝒎 The number of conversions of the loan n is computed using the formula n = tm

FORMULA: F = P(1 + i) n 𝑭 𝑷= 𝒏 (𝟏+𝒊)

I=F–P

Finding the Future Value Finding the Principal or the Present Value Finding the Interest

EXAMPLE: 1. Esther deposited P25 , 000 in a savings bank on January 13, 2013. At that time the bank was paying 4% interest compounded quarterly. On

July 13, 2015, the bank announced that it would start paying 4.5% interest, compounded quarterly. How much did Esther have to her credit on July 13, 2017. Solution: We have to computer for two separate compound amounts. We need to deal first with the first condition that the interest is at 4 % compounded quartery that will run from January 13, 2013 to July 13, 2015. F1 ?

P1 P25, 000 as of January 13, 2013

j1 4% = 0.04 in decimal

m1 4 (Quarterly) refer to Table 1.1

t1 1 ½ years = 1.5 years (from January 13, 2013 to July 13, 2015)

i1 𝑗 𝑖= 𝑚 0.04 𝑖= 4 𝑖 = 0.01

n1 n = tm n= 1.5(4) n= 6

Using the formula F1= P(1 + i)n F1= 25, 000(1 +0.01) 6 F1= 25, 000(1.01)6 F1= 25, 000(1.061520150) F1= P26, 538.00 We can now compute the compound amount at 4.5% interest compounded quarterly from July 13, 2015 to July 13, 2017. F2 ?

P2 P26, 538 as of July 13, 2015

j2 4.5% = 0.045 in decimal

m2 4 (Quarterly) refer to Table 1.1

t2 2 years = 2 years (from July 13, 2015 to July 13, 2017)

i2 𝑗 𝑖= 𝑚 0.045 𝑖= 4 𝑖 = 0.01125

n2 n = tm n= 2(4) n= 8

Using the formula F2= P(1 + i)n F2= 26, 538(1 +0.01125) 8 F1= 26, 538(1.01125) 8 F1= 26, 538(1.093624616) F1= P29, 022.61 Therefore, Esther have P29, 022.61 to her credit on July 13, 2017. 2. Bathsheba wants to provide a P200,000.00 graduation gift for her daughter Magdalene who is now 16 years old. She would like the fund to be available by the time her daughter is 20. She decides on an investment that pays 10% compounded quarterly. How large must the deposit be?

Solution: Given F P P200,000 ?

j 10% = 0.1 in decimal

m 4 (Quarterly) refer to Table 1.1

t 4 years (20 y/o 16 y/o now)

i 𝑗 𝑖= 𝑚 0.1 𝑖= 4 𝑖 = 0.025

n n = tm n= 4(4) n= 16

Using the formula: 𝑭 𝑷= 𝒏 𝑷=

(𝟏+𝒊) 𝟐𝟎𝟎,𝟎𝟎𝟎

(𝟏+𝟎.𝟎𝟐𝟓)𝟏𝟔 𝟐𝟎𝟎,𝟎𝟎𝟎 𝑷 = (𝟏.𝟎𝟐𝟓)𝟏𝟔 𝟐𝟎𝟎,𝟎𝟎𝟎 𝑷 = 𝟏.𝟒𝟖𝟒𝟓

𝑷 = 𝑷𝟏𝟑𝟒, 𝟕𝟐𝟓. 𝟓𝟎 Basheba should deposit P134, 725.50 in order to grow as much as P200, 000 by the time her daughter is 20 years old. 3. Salome paid P8, 600 on a loan made 2 years before at 6% compounded bimonthly. Find the interest generated.

F 8,600

Solution: Given P j ? 6% = 0.06 in decimal

m 6 (Bimonthly) refer to Table 1.1

t 2 years

i 𝑗 𝑖= 𝑚 0.06 𝑖= 6 𝑖 = 0.01

n n = tm n= 2(6) n= 12

We will begin by solving the value of P using the Formula 𝑭 𝑷= 𝒏 (𝟏+𝒊)

𝑷= 𝑷=

𝟖,𝟔𝟎𝟎 (𝟏+𝟎.𝟎𝟏)𝟏𝟐 𝟖,𝟔𝟎𝟎 (𝟏.𝟎𝟏)𝟏𝟐 𝟖,𝟔𝟎𝟎 𝟏.𝟏𝟐𝟔𝟖

𝑷= 𝑷 = 𝑷𝟕, 𝟔𝟑𝟐. 𝟐𝟑 After obtaining the value of P = P7, 632.23 and given the value of F= 8, 600, we can now compute I using the formula, I = F- P I = 8, 600 – 7, 632.23 I = 967.77 Salome’s loan earned an interest of P967.77.

ACTIVITY CARD 1 Complete the table for each given problem. 1. To what sum of money will P10, 000 accumulate in 3 years and 6 months at 5% compounded quarterly? Complete the table. F

P

j

m

t

i 𝑗 𝑖= 𝑚 12 𝑖= 14 𝑖=

n n = tm n= n=

2. An obligation of P27, 300 is due on March 16, 2017. What is the value of this obligation on November 16, 2014 at 18% compounded bimonthly?

F

Complete the table. P j

m

t

i 𝑗 𝑖= 𝑚 12 𝑖= 14 𝑖=

n n = tm n= n=

3. Find the interest charged on a loan of P10, 900 fofr 3 years at 7% compounded semiannually.

F

Complete the table. P j

m

t

i 𝑗 𝑖= 𝑚 12 𝑖= 14 𝑖=

n n = tm n= n=

ASSESSMENT CARD Read and analyze the problem below. Identify what is being ask in the given problem and put a  mark to its corresponding column. Problem 1. If money is worth 10% converted quarterly, find the interest of P33, 000 due at the end of 4 years. 2. Hannah bought a component from a friend and paid P10, 000 cash and agreed to pay P9, 000 two years later. At 9% compounded monthly, find the cash value of the component. 3. Andrew inherited P1, 500 on the day he became 35 years old. Under the specifications of the will, the money was placed in a trust fund that earned interest at 12.8% compounded quarterly. What amount was in the fund on Andrew,s fortieth birthday. 4. On March 15, 2013, a man borrowed P36, 000 and promised to pay the principal and interest at 11% compounded quarterly on September 15, 2016. How much will he pay? 5. In his will a San Sebastian alumnus appointed a trust company to handle his estates. The company was instructed to set aside a sum in a separate account sufficient to pay his alma mater P10, 000 at the end of 30 years. What sum should the company deposit in the separate account if it earns 7.5% converted semiannually?

Future Value

Present Value/Principal

Interest

ENRICHMENT CARD Solve the given problem. Complete the table and fill in the blanks. To what sum of money will P10, 000 accumulate in 3 years and 6 months at 5% compounded quarterly? F

P

j

m

t

i 𝑗 𝑖= 𝑚 12 𝑖= 14 𝑖=

Using the formula F= P(1 + i)n F= ______(1 +0.0125)14 F= 10, 000(1.0125)__ F= 10, 000(________) F= P___________

n n = tm n= n=

ANSWER KEY CARD Activity Card 1 1. F = ? P = 10 000 j= 0.05 i=0.0125 n=14 2. F = 27 300 P = ? j= 0.18 i=0.03 n=13.98 3. F = ? P = 10 000 j= 0.07 i=0.035 n=6

m=4t=3.5 m=6t=2.33 m=2t=3

Activity Card 2 1. Interest 2. Present Value/Principal 3. Future Value 4. Future Value 5. Present Value/Principal Enrichment Card 3 F=? P = 10 000 i=0.0125 n=14

F= F= F= F= F=

j= 0.05

Using the formula P(1 + i)n 10 000(1 +0.0125)14 10, 000(1.0125)14 10, 000(1.19) P11, 899.55

m=4t=3.5

REFERENCE CARD General Mathematics for Senior High School A Comprehensive Approach K to 12 Curriculum Compliant Winston S. Sirug, Ph.D. pp 126-156...