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Interest
1. Simple interest is interest paid on the principal amount only and not on accumulated interest. The simple interest formula is I=PRT, where I is interest, P is principal, R is interest rate, and T is time. 2. Compound interest is interest paid on the principal as well as on previously accumulated interest. The amount of compound interest is calculated using the formula A=P(1+R/n)^(n*t), where A is total amount, P is principal, R is annual interest rate, n is number of compounding periods per year, and t is time in years. 3. An annuity is a series of regular payments made at fixed time intervals. The
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Interest
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- 5. The amount paidat stated rate for use of money for specific time. we can also say that the rent.Simple interest is most often used for loans of shorter duration. Charge of borrowed money at annual percentage rate is interest. The money borrowed in a loan is called the principal. The number of dollars received by the borrower is the present value. In a simple interest loan, the principal and present value are the same. The interest rate is the fee for a simple interest loan and usually is expressed as a present of the principal. Simple interest is paid on the principal borrowed and not paid on interest already earned. 5
- 6. The simple interestof a loan can be calculated using the following formula. P = principal (amount borrowed) r = interest rate per year (in decimal form) t = time in years. 6
- 7. Find simple intereston an amount of Rs 800 in 8 month’ As we know formula I= 800*.05*8/12= 26.67 answer Hence interest is 26.67 7
- 8. An individual borrows$300 for 6 months at 1% simple interest per month. How much interest is paid? Remember to check that r and t are consistent in time units. Here, it will be months. I = Prt = 300 0.01 6 = $18 Assume you invest $1,000 at 6% simple interest for 3 years. ($1,000 .06 3 = $180) (or $60 each year. You would earn $180 interest. for 3 years) 8
- 9. where I isthe amount of interest, P is the principal (amount of money borrowed), r is the interest rate (per year), and t is the time (expressed in years). The formula can also be expressed as: 9
- 10. A loan madeat simple interest requires that the borrower pay back the sum borrowed (principal) plus the interest. This total is called the future value, or amount and is equal to P + I. where P + Prt P(1 + rt) P = principal or present value r = annual interest rate (in decimal form) t = time in years A = amount or future value 10
- 11. Find the futurevalue of $460 in 8 months, if the annual interest rate is 12%. A = P (1 + rt ) If you can earn 6% interest, what lump sum must be deposited now so that its value will be $3500 after 9 months? A = P (1 + rt ) 11
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- 13. Interest paid onprincipal plus interest is called compound interest it can be done semiannually, quarterly, monthly, or daily. This time interval is called the compounding period (or the period). Compound interest is based on the principal which changes from time to time The unpaid interest is added to the principal balance and becomes part of the new principal balance for the next interest period. 13
- 14. Period Interest Credited Times Credited per year 1 Rate per compounding period R Annual year Semiannual 6months 2 R 2 Quarterly quarter 4 R 4 Monthly month 12 R 12 14
- 15. Amount : CompoundInterest Where and A = amount or future value at the end of n periods P = principal or present value r = annual nominal rate m = number of compounding periods per year i = rate per compounding period n = total number of compounding periods 15
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- 17. Suppose $800 isinvested at 6%, and it is compounded annually. What is the amount in the account at the end of 4 years? ` First, determine the information that is given There will be $1009.98 in the account after 4 years. 17
- 18. The general formulafor finding the amount after a specified number of compound periods is where r = annual interest rate m = number of times compounded per year i = r/m = interest rate per period n = mt, the number of periods, where t is the number of years A = amount (future value) at the end of n compound periods P = principal (present value) 18
- 19. Interest earned onthe principal investment Earning interest on interest Principal plus interest 19
- 20. the difference between simpleinterest and compound interest on a certain sum is Rs 250for two years at 5% P.a find the sum? T= 2 years R=.05 P=? I=PRT P=.05*2 I=.10 C.I=P(1+I^N)-1 C.I=10(1+.05^2)-1 C.I=.1025 C.I –S.I 0.1025-.10=.0025 250/.0025=10000 The sum is 10000 20
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- 22. a sequence ofpayments made at regular time intervals. payments made at the end of each payment period. payment period coincides with the interest conversion period. 22
- 23. The future valueS of an annuity of n payments of R dollars each, paid at the end of each investment period into an account that earns interest at the rate of i per period is S R (1 i) n 1 i 23
- 24. The present valueP of an annuity of n payments of R dollars each, paid at the end of each investment period into an account that earns interest at the rate of i per period is P R 1 (1 i) n i 24
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Editor's Notes
- #2 (Advanced)To reproduce the shape effects on this slide, do the following:On the Home tab, in the Slides group, click Layout, and then click Blank.On the Home tab, in the Drawing group, click Shapes, and then under Rectangles, click Rectangle (first option from the left). On the slide, drag to draw a rectangle.Under Drawing Tools, on the Format tab, in the Size group, do the following:In the Shape Height box, enter 3”.In the Shape Width box, enter 3”.On the Home tab, in the bottom right corner of the Drawing group, click the Format Shape dialog box launcher. In the Format Shape dialog box, click Fill in the left pane, and then in the Fill pane, select Picture or texture fill. Click the button next to Texture, and then click Oak (fifth row, third option from the left).Also in the Format Shape dialog box, click Line Color in the left pane, and then in the Line Color pane, then select No line. Also in the Format Shape dialog box, click 3-D Rotation in the left pane, and then in the 3-D Rotation pane, do the following:Click the button next to Presets, and then under Perspective click Perspective Left (first row, second option from the left).In the X box, enter 40°.In the Y box, enter 10°.In the Perspective box, enter 20°.Also in the Format Shape dialog box, click 3-D Format in the left pane, and then in the 3-D Format pane, do the following:Under Bevel, click the button next to Top, and then under Bevel click Circle (first row, first option from the left). Click the button next to Bottom, and then under Bevel click Circle (first row, first option from the left). Under Depth, in the Depth box, enter 200 pt. Under Surface, click the button next to Material, and then under Standard, click Warm Matte (second option from the left). Click the button next to Lighting, and then under Neutral, click Soft (first row, third option from the left). In the Angle box, enter 270°.Also in the Format Shape dialog box, click Shadow in the left pane, and then in the Shadow pane, click the button next to Presets, and then under Perspective, click Perspective Diagonal Upper Right (first row, second option from the left). To reproduce the text effects on this slide, do the following:On the slide, right-click the rounded rectangle, click Edit Text, then enter text. Select the text. On the Home tab, in the Font group, select Arial Rounded MT Bold from the Font list, and then select 36 from the Font Size list.On the Home tab, in the Paragraph group, click Center to center the text within the rectangle.Under Drawing Tools, on the Format tab, in the bottom right corner of the WordArt Styles group, click the Format Text Effects dialog box launcher. In the Format Text Effects dialog box, click Text Fill in the left pane, and then in the Text Fill pane, do the following:Select Solid fill. Click the button next to Color, click More Colors, and then in the Colors dialog box, on the Custom tab, enter values for Red: 130, Green: 101, and Blue: 58.Also in the Format Text Effects dialog box, click Shadow in the left pane, and then in the Shadow pane, do the following:Click the button next to Presets, and then under Inner click Inside Diagonal Top Left (first row, first option from the left).In the Transparency box, enter 25%.In the Distance box, enter 5 pt. To reproduce the background on this slide, do the following:Right-click the slide background area, and then click Format Background. In the Format Background dialog box, click Fill in the left pane, select Gradient fill in the Fill pane, and then do the following:In the Type list, select Linear.Click the button next to Direction, and then click Linear Down (first row, second option from the left).Under Gradient stops, , click Add gradient stops or Remove gradient stops until four stops appear in the slider.Also under Gradient stops, customize the gradient stops that you added as follows:Select the first stop in the slider, and then do the following:In the Position box, enter 0%.Click the button next to Color, click More Colors, and then in the Colors dialog box, on the Custom tab, enter values for Red: 196, Green: 178, and Blue: 152.Select the second stop in the slider, and then do the following:In the Position box, enter 45%.Click the button next to Color, and then under Theme Colors click Tan, Background 2, Darker 90% (sixth row, third option from the left).Select the third stop in the slider, and then do the following:In the Position box, enter 72%.Click the button next to Color, click More Colors, and then in the Colors dialog box, on the Custom tab, enter values for Red: 66, Green: 62, and Blue: 50.Select the fourth stop in the slider, and then do the following:In the Position box, enter 100%.Click the button next to Color, click More Colors, and then in the Colors dialog box, on the Custom tab, enter values for Red: 149, Green: 128, and Blue: 107.