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# Simple Interest and Compound Interest Questions Answers

**GENERAL INSTRUCTIONS:**

- Exercises to perform them individually. In a way that can demonstrate mastery of the material.
- Write the used formula and the development of it.
- Use four decimal places. Convert to dollars and cents, or %, whatever the requested answer.
- Emphasize by circulating (or otherwise) the answer, for each required, if there is more than one.

**SIMPLE INTEREST:**

- How much is the amount and the total accumulated interest of$18.950; to 6. 585% for seven years and nine months?
- Find the difference between exact simple interest and ordinary simple interest when calculating$15,180to 8. 625%for 60-day space?
- If you deposited$1,8,750 at what %, you would accrue an amount of$57,156.25 in five years?

*In the case that is calculated ordinary simple considers 360 days and simple exact considers 365 days.*

**COMPOSED INTERS: (annual and parts of the year)**

- Find the amount and compound interest of$57,250 to 5 1/4% for 10-year space calculated:
- Annually
- Biannually
- Quarterly
- Continuously

Cuánto dinero necesita usted depositar en su cuenta de inversiones to have $100,000 after twenty-five years at 5.45% interest calculated annually?

**PRESENT VALUE:**

- Find the net present present value of an inheritance to be received within 15 years of$90,125discounted today at 4 3 /8%.
- From accepting the answer from 1 above, what interest or greater would be accepted today to reach $135,000 in 20 years.
- The property you bought 12years ago for$1,85,000, is now worth $225,000. What is the rate of return on your investment?
- Joe Doe deposited$25.500 into his savings account. The interest rate is 5%compound annually. How long will it take for the investment to reach $75.000?
- You have deposited$20,000 in stock investments, after three years, the balance of the investment is$180,900. What and how much has been the rate of return?

**Annuities:**

- If you and your partner decide toopen an IRA of$6,500 a year each. You are offered a 5 1/2% annual interest for 3 0years. How much will be the amount and accumulated interest on the annuity?
**VALUE PRESENT OF AN ANNUITY:**- You're lucky enough to stick with the Parrot. The prize is 2 million. You have the option (1) to receive a single amount once, (2) receive an identical annuity each year, for 20 years. Ignore the tax. Discount rate 4.5%
- What is the present value of option (1)?
- What is the present value of option (2)?
- Which one would you select and why?

## Answer

**GENERAL INSTRUCTIONS:**

- Exercises to perform them individually. In a way that can demonstrate mastery of the material.
- Write the used formula and the development of it.
- Use four decimal places. Convert to dollars and cents, or %, whatever the requested answer.
- Emphasize by circulating (or otherwise) the answer, for each required, if there is more than one.

**SIMPLE INTEREST:**

- How much is the amount and the total accumulated interest of$18.950; to 6. 585% for seven years and nine months?

**Answer:**

SI = (PxTxR)/100

P = $18.950

R = 6.585%

T= 7 years 9 months = 7+9/12 = 7+0.75= 7.75yeas

SI = 18.950*6.585*7.75/100 = $9.6709

Amount = P+SI = 18.950+9.6709 = $28.6209

Find the difference between exact simple interest and ordinary simple interest when calculating$15,180to 8. 625%for 60-day space?

**Answer:**

Ordinary simple interest is a simple interest that uses 360 days as the equivalent number of days in a year. On the other hand, Exact** **simple interest is a simple interest that uses exact number of days in a year which is 365 (or 366 for leap year).

**Ordinary simple interest** :

SI = (PxTxR)/100

P = $15180

R = 8.625%

T= 60 days = 60/360 years

SI = (15180*8.625*60/360)/100 = $218.2125

Amount = P+SI = 15180+218.2125 = $15,398.2125

**Exact simple interest** :

SI = (PxTxR)/100

P = $15180

R = 8.625%

T= 60 days = 60/365 years

SI = (15180*8.625*60/365)/100 = $215.2233

Amount = P+SI = 15180+215.2233 = $15,395.2233

If you deposited$1,8,750 at what %, you would accrue an amount of$57,156.25 in five years?

Answer:

Amount = $57,156.25

P = $18,750

SI = Amount – P = 57,156.25- 18,750 = 38,406.25

SI = PxTxR/100

38,406.25 = 18,750*R*5/100

R = 38,406.25/(18,750*5) = 0.4096667 = 40.96667%

*In the case that is calculated ordinary simple considers 360 days and simple exact considers 365 days.*

**COMPOSED INTERS: (annual and parts of the year)**

Find the amount and compound interest of$57,250 to 5 1/4% for 10-year space calculated:

**Answer:**

Compound Interest = Total amount of Principal and Interest in future (or Future Value) *less* Principal amount at present (or Present Value)

**= [P (1 + ***i/n***)**^{nt}**] – P**

(Where P = Principal, *i* = nominal annual interest rate in percentage terms, and n = number of compounding periods in a yeasr and t = number of years.)

Annually:

P = 57,250

i = 5.25%

n =1

t = 10

Amount = 57,250 (1+0.0525/1)^(10*1)

= $95,498.50

CI = $95,498.50 – 57,250 = $38,248.50

Biannually

P = 57,250

i = 5.25%

n =2

t = 10

Amount = 57,250 (1+0.0525/2)^(10*2)

= $96,125.5625

CI = $95,125.5625 – 57,250 = $38,875.5624

Quarterly

P = 57,250

i = 5.25%

n =4

t = 10

Amount = 57,250 (1+0.0525/4)^(10*4)

= $96,448.7889

CI = $96,448.7889 – 57,250 = $39,198.7889

Continuously

Amunt = P*s^rt

P = 57,250

r = 5.25%

t = 10 years

e = exponential series

Amount = 57,250* e^(5.25%*10) = $96,778.7691

CI = $96,778.7691 – 57,250 = $39,528.7691

Cuánto dinero necesita usted depositar en su cuenta de inversiones to have $100,000 after twenty-five years at 5.45% interest calculated annually?

**Answer:**

Amount **= [P (1 + ***i/n***)**^{nt}**] **

(Where P = Principal, *i* = nominal annual interest rate in percentage terms, and n = number of compounding periods in a yeasr and t = number of years.)

Annually:

P = ?

i = 5.45%

n =1

t = 25

Amount = $100,000

100,000 = P* (1+0.0545/1)^(25*1)

P = 100,000 /(1+0.0545/1)^(25*1

= $26,535.9963

$26,535.9963 when invested for 25 years @5.45% calculated annually will amount to $100,000

**PRESENT VALUE:**

Find the net present present value of an inheritance to be received within 15 years of$90,125discounted today at 4 3 /8%.

**Answer:**

NPV = FV/(1+r)^t

Where,

NPV = Net present Valúe

FV = Future value = $90,125

R = 4 3/8% = 4.375%

NPV = 90125/ (1+0.04375)^15

= $47,413.06

From accepting the answer from 1 above, what interest or greater would be accepted today to reach $135,000 in 20 years.

**Answer:**

NPV = FV/(1+r)^t

Where,

NPV = Net present Valúe = $47,413.06

FV = Future value = $135,000

R = ¿

47,413.06 = 135,000/ (1+r)^15

R = 7.2249%

The property you bought 12years ago for$1,85,000, is now worth $225,000. What is the rate of return on your investment?

**Answer:**

NPV = FV/(1+r)^t

Where,

NPV = Net present Valúe = $185000

FV = Future value = $225,000

R = ¿

185,000 = 225,000/ (1+r)^12

R = 1.6445%

Joe Doe deposited$25.500 into his savings account. The interest rate is 5%compound annually. How long will it take for the investment to reach $75.000?

**Answer:**

Future Amount = Total amount of Principal + Interest in future (or Future Value)

**= [P (1 + ***i/n***)**^{nt}**] **

(Where P = Principal, *i* = nominal annual interest rate in percentage terms, and n = number of compounding periods in a yeasr and t = number of years.)

P =25.500

i= 5%

n =1

t = ?

75.000 = 25.500 (1+0.0500/1)^t

t = 22.1112years

It will take 22.1112 years for the investment to reach $75.000

You have deposited$20,000 in stock investments, after three years, the balance of the investment is$180,900. What and how much has been the rate of return?

**Answer:**

**Simple Interest:**

Amount = PxTxR/100

180,900 = 20,000*3*R/100

R = 180,900*100/20,000*3

= 301.5%

The interest rate is 301.5% if compounded annually

**Compounded Annually:**

Future Amount = Total amount of Principal + Interest in future (or Future Value)

**= [P (1 + ***i***)**^{t}**] **

*i* = nominal annual interest rate in percentage terms, and n = number of compounding periods in a yeasr and t = number of years.)

P =20,000

i= ?%

t = 3 years

Amount = 180,900

180,900 = 20,000 (1+i)^3

i =108.355%

The interest rate is 108.355% if compounded annually

**Annuities:**

If you and your partner decide toopen an IRA of$6,500 a year each. You are offered a 5 1/2% annual interest for 3 0years. How much will be the amount and accumulated interest on the annuity?

**Answer:**

Annuity Due:

P = PMT x (((1 + r) ^ n) / r)

Here is what the variables represent:

- P = the future value of the annuity = ¿
- PMT = the value of each annuity payment = 6500
- r = the interest rate = 5.50%
- n = the number of periods over which payments will be made = 30 years

P = 6500 x(((1+5.5%)^30)/5.50%)

Amount = $470,830.61

Accumulatted Interest = 275,830.61

**Note: The investment is made at the end of the year. **

If investment is made at begining of the year (immediate annuity):

Amount = $496,726.29

Accumulated Interest = $301.726.29

Reference table:

Year | Installment | Principle | Interest | Amount |

| | | 5.50% | |

1 | 6500 | 6,500.00 | 357.50 | 6,857.50 |

2 | 6500 | 13,357.50 | 734.66 | 14,092.16 |

3 | 6500 | 20,592.16 | 1,132.57 | 21,724.73 |

4 | 6500 | 28,224.73 | 1,552.36 | 29,777.09 |

5 | 6500 | 36,277.09 | 1,995.24 | 38,272.33 |

6 | 6500 | 44,772.33 | 2,462.48 | 47,234.81 |

7 | 6500 | 53,734.81 | 2,955.41 | 56,690.22 |

8 | 6500 | 63,190.22 | 3,475.46 | 66,665.69 |

9 | 6500 | 73,165.69 | 4,024.11 | 77,189.80 |

10 | 6500 | 83,689.80 | 4,602.94 | 88,292.74 |

11 | 6500 | 94,792.74 | 5,213.60 | 1,00,006.34 |

12 | 6500 | 1,06,506.34 | 5,857.85 | 1,12,364.19 |

13 | 6500 | 1,18,864.19 | 6,537.53 | 1,25,401.72 |

14 | 6500 | 1,31,901.72 | 7,254.59 | 1,39,156.31 |

15 | 6500 | 1,45,656.31 | 8,011.10 | 1,53,667.41 |

16 | 6500 | 1,60,167.41 | 8,809.21 | 1,68,976.62 |

17 | 6500 | 1,75,476.62 | 9,651.21 | 1,85,127.83 |

18 | 6500 | 1,91,627.83 | 10,539.53 | 2,02,167.36 |

19 | 6500 | 2,08,667.36 | 11,476.70 | 2,20,144.07 |

20 | 6500 | 2,26,644.07 | 12,465.42 | 2,39,109.49 |

21 | 6500 | 2,45,609.49 | 13,508.52 | 2,59,118.01 |

22 | 6500 | 2,65,618.01 | 14,608.99 | 2,80,227.00 |

23 | 6500 | 2,86,727.00 | 15,769.99 | 3,02,496.99 |

24 | 6500 | 3,08,996.99 | 16,994.83 | 3,25,991.82 |

25 | 6500 | 3,32,491.82 | 18,287.05 | 3,50,778.87 |

26 | 6500 | 3,57,278.87 | 19,650.34 | 3,76,929.21 |

27 | 6500 | 3,83,429.21 | 21,088.61 | 4,04,517.82 |

28 | 6500 | 4,11,017.82 | 22,605.98 | 4,33,623.80 |

29 | 6500 | 4,40,123.80 | 24,206.81 | 4,64,330.61 |

30 | 6500 | 4,70,830.61 | 25,895.68 | 4,96,726.29 |

Total | 195000 | | 301726.29 | 4,96,726.29 |

**VALUE PRESENT OF AN ANNUITY:**

You're lucky enough to stick with the Parrot. The prize is 2 million. You have the option (1) to receive a single amount once, (2) receive an identical annuity each year, for 20 years. Ignore the tax. Discount rate 4.5%

- What is the present value of option (1)?
- What is the present value of option (2)?
- Which one would you select and why?

**Answer:**

- NPV = Net Present value = $2 million
- Present value of annuity:

PV = PMT x (((1 – (1 + r) ^ -n) / r)

P V= the present value of the annuity = ¿

PMT = the value of each annuity payment = 2million/20 = $100,000

r = the discount rate = 4.5%

n = the number of periods over which payments will be made = 20 years

PV = 100000 x((1-(1+4.5%)^-20)/4.50%)

= 1,359,329.366

*Payment is made at the begining of the year (immediate annuity)

Option 1 is better as the NPV of the amount is higher and hence has higher worth.

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