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Simple Interest and Compound Interest Questions Answers


GENERAL INSTRUCTIONS:

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

SIMPLE INTEREST:

  1. How much is the amount and the total accumulated interest of$18.950; to  6. 585% for  seven  years and  nine  months?
  2. Find the difference between exact simple interest and ordinary simple interest when calculating$15,180to  8. 625%for 60-day space?  
  3. 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)

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

  1. Find the net present present value of an inheritance to be received within 15 years of$90,125discounted today at  4  3 /8%.
  2. From accepting the answer from 1 above, what interest or greater would be accepted today to reach $135,000 in 20  years.
  3. The property you bought 12years ago for$1,85,000, is now worth $225,000. What is the rate of return on your investment?
  4. 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?
  5. 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:

  1. 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?  
  2. VALUE PRESENT OF AN ANNUITY:
  3. 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%
    1. What is the present value of option (1)?
    2. What is the present value of option (2)?
    3. Which one would you select and why?

Answer

GENERAL INSTRUCTIONS:

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

SIMPLE INTEREST:

  1. 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

(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 =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%

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

Answer:

  1. NPV = Net Present value =  $2 million
  2. 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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