Tips for using your calculator in compound interest ...



Tips for using your calculator in compound interest calculations.

There are basically 4 types of problems that involve 4 different versions of the compound interest formula. The basics of using the two types of calculator were first covered in Module 2 and should be reviewed.

Version 1

[pic]is used when P, I, n and Y are given.

|Find T if P = 1000, I = .05, Y = 12 and n = 52 |

| |

|The formula with the given values is: |

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|[pic] The rest is done on a calculator. |

|Operations on a Common Calculator |Operations on a Display Calculator |

|1) Work inside the parenthesis first and follow the order of |1) Work inside the parenthesis first. |

|operations. | |

|[pic] |Enter 1 + .05 (52 |

|This number will come up in scientific notation on most | |

|calculators so add 1 to it right away and you’ll get the decimal |Press “=” or enter and the display will read 1.0009615 |

|equivalent. | |

| |2) Use the exponent |

|.0009615 + 1 = 1.009615 | |

| |The display calculator will allow you insert groups as exponents |

|We now have [pic] |so press the “^” button and then enter (12 “times” 52) |

| | |

|2) Find the exponent. (12)(52) = 624 |Press “enter” and the display should read 1.812549926 |

| | |

|We now have [pic] |3) Multiply by 1000 to get the final answer. |

| | |

|3) Use the exponent. | |

| | |

|You have to use the xy or yx button on your calculator. | |

|Enter 1.0009615. Press xy. Enter 624. | |

|Press “=” or “enter”. | |

| | |

|We now have [pic]=1821.5 | |

|The goal in working these problems should be to do as much of the work as possible on the calculator without writing any numbers |

|down. The display calculator will allow you to complete every problem without writing anything down. The common calculator can work|

|the same way if you calculate the exponent first. |

Version 2

[pic] is used when T, P, Y and n are given.

|Find I if P = 1000, T = 3000, Y = 20 and n = 26. |

| |

|The formula with the given values is: [pic] |

|Operations on a Common Calculator |Operations on a Display Calculator |

| | |

|1) Simplify the fraction. [pic] |1) Simplify the fraction. [pic] |

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|2) The trickiest part is the fraction exponent. |2) Use the exponent. |

| | |

|Multiply 20 ( 26 = 520 |Enter 3 > Press “^” > Enter (20 times 26) > Press the x-1 button.|

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|Locate the 1/x or x-1 button. |The display should read: 3^(20*26)-1 |

| | |

|Enter 3> Press xy button > Enter 520 > Press the 1/x or x-1 |Press “enter” or “=” and the display should read: 1.002114949. |

|button and the display will read .0019230769. (This is equal to | |

|1/520.) |Leave this on the display. |

| | |

|Press “=” or “enter” and the display will read 1.002114949. |3) Finish the problem. |

| | |

|Leave this on the display. |Press – 1: Display reads: “Ans – 1” |

| | |

|3) Finish the problem. |Press “enter”: Display reads: .002114949 |

| | |

|Subtract 1. Display reads. .002114949 |Multiply by 26: Display reads “Ans * 26” |

| | |

|Multiply by 26. Display reads .0549886817 |Press “enter”: Display reads .0549886817 |

| | |

|Thus, I = 5.5% |Thus, I = 5.5% |

| | |

|A person who wants a $1,000 investment to grow to $3,000 in 20 years must get an interest rate of 5.5% that compounds biweekly. |

Version 3

[pic] is used when T, I, n and Y are given.

|Find P if T = 12000, I = .055, n = 365 and Y = 12. |

| |

|The formula with the given values is: [pic] |

| |

|This one is pretty straight forward. Follow these steps and you can do most of this on your calculator. |

|Operations on a Common Calculator |Operations on a Display Calculator |

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|Step 1 Simplify the exponent. |On the calculator: |

| | |

|12 ( 365 = 4380 |Enter .055 and divide by 365. Add 1. |

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|Step 2 The rest can be done on the calculator. |Display reads: 1.000150685 |

| | |

|Enter .055 ( 365 and add 1. |Enter: ^ (12*365) Hit “enter” or “=” |

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|Display reads: 1.000150685 |Display reads: 1.934696137 |

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|Press the xy button and enter 4380. Press “=”. |Press the 1/x or x-1 button. This converts the division to |

| |multiplication. |

|Display reads: 1.934696137 | |

| |Press “enter”: Display reads: .5168770335 |

|Press the 1/x or x-1 button. This converts the division to | |

|multiplication. |Multiply by 12000 and the result is 6202.524402. |

| | |

|Display: .5168770335 | |

| | |

|Multiply by 12000 | |

| | |

|Result: 6202.524402 | |

|Thus, P = 6202.52. A person that invests $6202.52 at 5.5% interest that compounds daily will have $12,000 in 12 years. |

Version 4

[pic] is used when T, P, I and n are given.

|Find Y if T = 12000, P = 2000, I = .055 and n = 365. |

| |

|The formula with the given values is: [pic] |

|Operations on a Common Calculator |Operations on a Display Calculator |

|The log function is just a button to press on your calculator. |The log function is just a button to press on your calculator. |

|You simplify the parenthesis, press the log button and that part |The display calculator allows you to do several operations at |

|of the problem is solved. |once so follow these steps to use the log function. |

| |Work on the denominator. |

|Step 1 Simplify the parenthesis in the numerator. 12000/2000 =| |

|6 |Press “log” and enter (1 + .055 (365) |

| | |

|Step 2 Work on the denominator. |Press “Enter” and the display should read: |

| | |

|Find 1 + .055/365 |6.54367 E –5 This is scientific notation. It is equal to |

| |.0000654367. |

|You should get: 1.000150685 | |

| |Multiply by 365 |

|Press the “log” button and the display should read .0000654367 or| |

|it’s equivalent in scientific notation. |Display reads: .023884397 |

| | |

|Multiply by 365 and the display should read: .023884397 |Press the x-1 button to change the division to multiplication. |

| | |

|Step 3 Finish the problem |Display reads: 41.86833766 |

| | |

|Press the 1/x or x-1 button to change the division to |Press “multiplication” and the display will read: Ans * |

|multiplication. | |

| |Enter: log(12000/2000) |

|Display reads: 41.86833766 | |

| |Press “enter” and we have completed this calculation. |

|Press “multiply” and enter 6 from step 1. | |

|Do not press “enter” yet. | |

| | |

|Press “log” > Display reads: .7781512504 | |

|Press “enter”>Display reads: 32.5798993 | |

|Thus, Y = 32.5798993. It will take about 32.58 years for $2000 to grow into $12000 at 5.5% interest that compounds daily. |

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