Simple Interest And Compound Interest Questions Answers

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:

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.