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Simple Present
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practica realizada en la universidad autonoma de chiapas, la cual se realiza una tecnica basica realizada en reflujo, para purificar alcoholes, como la cerveza, donde nos muestra el proceso …Descripción completa
Interest is charge incurred when a loan or credit is obtained.
Simple Interest is the interest calculated on the original principal for the entire period it is borrowed or invested. The formula:
You borrowed RM 1,000 from a bank for one year and you paid back RM 1,080 at the end of that year. The additional amount of RM 80 is the charge or interest you need to pay when you borrow RM 1,000.
I = Prt where,
Interest rate is usually expressed as per cent (%) per annum There are two types of interest: Simple Interest and Compound Interest
I - simple interest (RM) P - principal (RM) (or amount invested or amount borrowed or present value) r - rate of interest (%) (per annum or per year) t - time or period (in years)
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SOLVING MATHEMATICAL SIMPLE INTEREST CONCEPT 1.
PROBLEMS
RM 1,000 is invested for four years in a bank, earning a simple interest rate of 8% per annum. Find the simple interest earned at the end of the fourth year.
I =? P = RM 1,000 r = 0.08 t = 4 years
2. Find the simple interest on RM 650 invested at 1 5.6% for 3 2 years. Solution:
RM 1,000
0
2
3
I =?
P = RM 650
4
r = 0.056 t =3 1 years 2
I = Prt I = (650)*(0.056)*( 3 1) 2 = RM 127.40
I= ?
I = Prt I = (1000)*(0.08)*(4) = RM 320 5
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USING
Solution:
Interest is money earned when money is invested. You deposited RM 1,000 in a bank for a year and you find at the end of year one, you have RM 1,050 in your account. The additional amount of RM 50 is the interest you earned when you invest RM 1,000.
INTRODUCTION
What is INTEREST?
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UiTM SARAWAK
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SIMPLE AMOUNT FORMULA The Simple Amount is the sum of the original principal and the interest earned. The formula is:
3. Find the simple interest on RM 15000 borrowed at the rate of 3% for 5 months.
Solution:
I =?
S Original Principal + Interest Earned
P = RM 15 000
S PI
S P Pr t
r = 0.03 t = 5 years 12
where,
I = Prt I = (15000)*(0.03)*( 5 ) 12 = RM 187.50 7
RM 10,000 is invested for 4 years 9 months in a bank earning a simple interest rate of 10% per annum. Find the simple amount at the end of the investment period.
Solution: P = RM 5000 t =3 S = RM 6125 r=
Solution:
S = P(1 + rt) 6125 = 5000 ( 1+ (3)) 6125 = 1+ 3
S=? P = RM 10,000 9
S - simple amount or maturity value or future value (RM) P- principal or amount invested or amount borrowed or present value (RM) r - rate of interest (%) (per annum or per year) 8 t - time or period (in years)
2. Aida invest RM 5,000 in an investment fund for three years. At the end of the investment period, his investment will be worth RM 6125. Find the simple interest rate that is offered.
SOLVING MATHEMATICAL PROBLEMS USING SIMPLE AMOUNT CONCEPT 1.
S P( 1 rt )
57
t = 4 12 12 r = 0.10 S = P(1 + rt)
5000 6125 -1=3 5000 57
= 10000(1+ (0.10)*( )) 12 = RM 14750
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r = 0.075 r = 0.075 * 100 r = 7.5%
3. How long does it take for an investment of RM1200, given the rate of interest is stated at 10% per annum to be worth RM 1260?
4. How much is the deposit for 2 years in a company that pays at an interest rate of 15% per annum in order to get an interest worth RM15000?
Solution:
Solution:
P = RM 1200 S = RM 1260 r = 0.1
t =2 r = 0.15 S = RM 15000 P=?
t =? S = P(1 + rt) 1260 = 1200 (1 + 0.1(t))
S = P(1 + rt) 15000 = P (1 + 0.15(2)) 15000 = 1.3 P P = RM 11538.46
(1260/1200 ) -1 = 0.1t 0.05/0.1 = t t = 0.5 years (or 6 months) 11
MARIATHY BT KARIM
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EXACT TIME AND APPROXIMATE TIME
EXAMPLE
CONCEPTS
DETAILS
1. Find the Exact time from 15 June 2011 to 23 October 2011.
Exact Time
It is exact number of days between any two given dates. Each specific month of the year that is involved is counted exactly as it is e.g. January = 31 days; February = 28 or 29 days;...
Approximate Time
Assume that a month has 30 in the calculation of number of days between two given dates.
Month June July August September October TOTAL
June July August September October TOTAL
Number of (Exact time) 30 – 15 =15 30 30 30 23 128
days
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3. Find the Exact time from 3rd May 2009 to 29 August 2009.
2. Find the Approximate time from 15 June 2011 to 23 October 2011. Month
Number of (Exact time) 30 – 15 =15 31 31 30 23 130
days
Month
Number of (Exact time) 31 – 3 = 28 30 31 29 118
May June July August TOTAL
days
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ORDINARY SIMPLE INTEREST AND EXACT SIMPLE INTEREST
4. Find the Approximate time from 3rd May 2009 to 29 August 2009. Month May June July August TOTAL
Number of (Exact time) 30 – 3 =27 30 30 29 116
CONCEPTS
DETAILS
Ordinary Simple Interest
t is based upon a 360 day year
days
Exact Simple t is based upon a 365 (depending on Interest whether it is a leap year or not) day year
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Using the exact time and ordinary simple interest also known as Banker’s Rule.
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EXAMPLE
P RM 2000
1. On 15th February 2012, Jamil deposited RM 2000 into a saving account. Using Banker’s Rule, determine the accumulated amount on 18 August 2012 if the interest rate was 9.89%. Month February March April May June July August Total
Number of Days 29 – 15 = 14 31 30 31 30 31 18 185
185 365 r 0.0989
t
S P (1 rt ) 2000(1 0.0989* RM 2101.65
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2. Find the amount interest using exact time and exact simple interest on a loan of RM 1000 made on the 13 January 2011 where the loan was paid on the 14 April 2011. Given that the simple interest rate was 4%. Month January February March April Total
185 ) 360
P RM 1000 91 365 r 0.04
t
I Pr t
Number of Days 31 – 13 = 18 28 31 14 91
1000(0.04)(
91 ) 365
RM 9.97
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PRESENT VALUE
3. An actor borrowed RM19000 from a bank on 17 May 2010 at 12% ordinary simple interest using approximate time. After a certain time, he paid back RM19316.67. Find the date of repayment.
Formula of present value:
P S (1 rt) 1
Answer : 7 July 2010.
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MARIATHY BT KARIM
Present Value is the value on a given date of a payment.
P
S
1 rt
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EXAMPLE
THANK YOU…….NEXT…..
1. Find the present value at 9% simple interest of a debt RM 4000 due in 8 months.
Tutorial 2 Pass Years Quiz 2
Answer: RM3773.58
2. Find the present value of a debt 100 days prior to its date of maturity at 8% exact simple interest with a maturity value of RM 2020. Answer: 1976.68
3. Ajay borrowed a certain amount of money at 7% simple interest. If he has to pay back RM3000 in 9 months, what is the actual amount that he borrowed? Answer: RM 2850.36