interest practice problems

7/31/2019 Interest Practice Problems

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I = P t r I = Interest RateP = Principal (the initial amount borrowed or deposited)t = Number of years/months/days the amount is deposited or borrowed forr = Annual rate of interest (percentage)

Examples

1Answer 848.25

2Answer 2565

3 Calculate the interest when Rs. 6300 is borrowed from March 15th, 2004 until January 20th 2005 atHINT:you will not count the day the money is borrowed or the day the money is returnedAnswer 428.05

4HINT:261/365 days is the calculation for the t - time.Answer 79.55

5

Answer 5%

6Answer 2075

7Answer 4050

8Answer Rs. 840

9

Answer

10Answer 3 Years

HINT:use 14/12 for time and move the 12 to the numerator in the formula r=I/Pt

What Sum of Money Can you Invest for 300 Days at 5.5% to Earn Rs.93.80?

How much money do I need (principal) to get Rs.18.20 at 3.25% in 8 months?

How many months will it take if I invest Rs.5000.00 at 5% to make Rs.136.48?

How many years will it take for Rs.745.00 to make Rs.178.80 at 8%?

0.54592 years or 6.55 months

SIMPLE INTEREST

Calculate the amount of interest on Rs.4500.00 when earning 9.5% per annum for six years.

Calculate the amount of interest on Rs.8700.00 when earning 3.25% per annum for three years.

What amount of principal will earn interest of Rs.175.50 at 6.5% in 8 months?

What's the Interest on Rs.890.00 at 12.5% for 261 Days?

What Annual Rate of Interest Is needed for Rs.2100.00 to earn Rs.122.50 in 14 Mths?


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P = I / t r

t = I / P r

r = I / P t

rate of 8%.


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Simple Interest - Solutions

1

Answer I = P n r

I = 848.25

2

Answer I = P n r

I = 2565

3 Calculate the interest when Rs. 6300 is borrowed from March 15th, 2004 until January 20th 200

Answer

I = P n rI = 6300 * .08 * 310/365

I = 428.06

4

Answer I = P n rI = 890 * .125 * 261/365I = 79.55

5

Answer r = I / Pn

r = 5%

6

Answer P = I / r n

P = 2075

Calculate the amount of interest on Rs. 8700.00 when earning 3.25% per annum for three years.

Calculate the amount of interest on Rs.4500.00 when earning 9.5% per annum for six years.

What's the Interest on Rs.890.00 at 12.5% for 261 Days?

I = 8700 * .0325 * 3

I = 4500 * .095 * 6

HINT:261/365 days is the calculation for t - time.

HINT:You will not count the day the money is borrowed or the day the money is returned.

What Annual Rate of Interest Is needed for Rs.2100.00 to earn Rs.122.50 in 14 Mths?

First calculate the total number of days for which the money is borrowed, excluding tand the day of return. It comes to 310 days. So, here, n would be, 310/365.

HINT:use 14/12 for time and move the 12 to the numerator in the formula r=I/Pt

P = 93.8 / (.055 * 300/365)

r = 122.5 / (2100 * 14/12)

What Sum of Money Can you Invest for 300 Days at 5.5% to Earn Rs.93.80?


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7

Answer P = I / r n

P = 4050

8

Answer P = I / r n$840.00

P = 840

9

Answer n = I / P r

10

Answer n = I / P rn = 178.8 / (745 * .08)n = 3 years

n = 136.48 / (5000*.05)

P = 175.5 / (.065 * 8/12)

What amount of principal will earn interest of Rs.175.50 at 6.5% in 8 months?

How many years will it take for Rs.745.00 to make Rs.178.80 at 8%?

n = .54592 years or 6.55 months

How many months will it take if I invest Rs.5000.00 at 5% to make Rs.136.48?

P = 18.2 / (.0325 * 8/12)

How much money do I need (principal) to get Rs.18.20 at 3.25% in 8 months?


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at a rate of 8%.

e day of borrowing


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Amount = Principal + Interest

A = the amount of money accumulated after n years, including

P = the

A = the i

r = the i

n = the

t = the n

Formula:

('n' approaches infinity)A = P e^(rt) e is approximately 2.71828

Examples

1

Answer A = 6802.44 and I = 1802.44

2

Answer 10600

3

Answer 10609

4

n = number of years the amount is deposited or borrowed for

If Interest is paid more frequently:

Monthly

P (1 + r)^1 = (annual compounding)

P (1 + r/4)^4 = (quarterly compounding)

P (1 + r/12)^12 = (monthly compounding)

COMPOUND INTEREST

A = P(1 + r)^n

Annually

Quarterly

P = Principal (the initial amount borrowed or deposit

r = annual rate of interest (percentage)

A = P (1 + r/n)^nt

P = Principal (the initial amount borrowed or deposit

r = annual rate of interest (percentage)

t = number of years the amount is deposited or borrowed for

n = the number of times per year that interest is compounded

A = the amount of money accumulated after n years, including

A third bank promises a similar interest rate with but the rate being compounded quarterly. F

earned through this bank.

If Interest is paid every secon

An amount of Rs.5000.00 is borrowed to purchase a car. Find out how much the

Rs.5000.00 is borrowed at an interest rate of 8% for 4 years.

A sum of Rs. 10000 is deposited in a bank which provides 6% interest rate. Find out the aminvestment with the interest being calculated annually.

Another bank promises the same interest rate with the interest being compounded semi-annbe earned through this bank.


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Answer 10613.64

5

Answer 10616.78

6

Answer 10618

7 Find the amount that can be earned if the same amount at the same interest rate is compouAnswer 10618.31

8 What would happen if the interest rate is compounded every moment?Answer 10618.37

A financial Institution promises a similar interest rate with a monthly compounding of interest

earned.

A businessman needs money and asks for a loan of a similar amount with a similar interest rand commits to pay an interest compounded weekly. Find the amount that can be earned atmoney is lent to this businessman.


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interest.

rincipal (current worth)

nitial amount on deposit

terest rate (expressed as a fraction: ex: 6% = .06)

umber of times per year that interest is compounded

umber of years invested

interest.

ind the amount that can be

car will cost if an amount of

unt that can be earned by this

ually. Find the amount that can


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ded daily.

. Find the amount that can be

ate. He is in dire need of moneythe end of one year if the same


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Compound Interest - Solutions

1

AnswerA =5000*(1.08)^4

2

Answer

A =10600

3

Answer

A = 10609

4

Answer

5

Answer

An amount of Rs.5000.00 is borrowed to purchase a car. Find out how much the car will cosborrowed at an interest rate of 8% for 4 years under compounding policy.

A sum of Rs. 10000 is deposited in a bank which provides 6% interest rate. Find out the am

investment at the end of one year with the interest being calculated annually.

Another bank promises the same interest rate with the interest being compounded semi-anbe earned through this bank at the end of one year .

A third bank promises a similar interest rate with but the rate being compounded quarterly.earned through this bank at the end of one year .

A =10000*(1.06) 1

A = 10000*(1+.06/2)^(2*1)

A = P(1 + r)^n

A = 6802.445

A = P (1 + r/n)^nt

Interest = Amount - PrincipalI = 6802.445 - 5000I = 1802.445

A = P(1 + r)^n

A = P (1 + r/n)^nt

A = 10000*(1+.06/4)^(4*1)A = 10613.64

A = P (1 + r/n)^nt

A financial Institution promises a similar interest rate with a monthly compounding of interes

earned at the end of one year .

A = 10000*(1+.06/12)^(12*1)A = 10616.78


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6

Answer

7

Answer10618.31

8

Answer

A = 10618.37

A = P e^(rt)

A = 10000*2.71828 (.06*1)

A businessman needs money and asks for a loan of a similar amount with a similar interestand commits to pay an interest compounded weekly. Find the amount that can be earned at

money is lent to this businessman.

A = P (1 + r/n)^nt

A = 10000*(1+.06/365)^(365*1)A = 10618.31

Find the amount that can be earned at the end of one year if the same amount at the samedaily.

A = P (1 + r/n)^nt

A = 10000*(1+.06/52)^(52*1)A = 10618

What would happen at the end of one year if the interest rate is compounded every moment


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t if an amount of Rs.5000.00 is

ount that can be earned by this

ually. Find the amount that can

ind the amount that can be

. Find the amount that can be


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rate. He is in dire need of moneythe end of one year if the same

interest rate is compounded

?


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Additional Problems

50 N65 Y57 N

500 N14588 Y8878 N

Principal = 152

SI 300

CI 347CI 349

compounded annually

SI for 100 years

SI for 10 years

compounded monthly

compounded annually

compounded quarterly

1. What is the better way to invest Rs.100 for ten years: at 5% simple interest, 4.8% inter

4.6% interest compounded annually? Does your answer change if the investment lasts 1

2. If you invest some money at 8% annual compound interest for five years and end up w

how much (to the nearest Rs.10) did you originally invest?

3. What is the difference between investing Rs.1000 for five years at 6% simple interest,

quarterly, and 6% interest compounded monthly?

CI for 10 years compounded monthly

CI for 100 years compounded monthly


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est compounded monthly, or

0 years?

ith approximately Rs.223,

6% interest compounded


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EMI Problems Equated Monthly Instalments

Present Value Interest of a Future Annuity at rate r and n period

PVIFA r,n = [(1+r) ^ n 1 ] / [r(1+r) ^ n ] A = FVAn / { [ (( 1+r)^n) - 1 ] / r }

Examples

1

Answer 314819.5

2

Answer 7220.665

3

Answer .69 percent

4

Answer 13 percent

5 What is the effective interest rate in the above case?

Answer 8.33 percent

6

Answer 16 percent

2836.788

7 What is the effective interest rate in the above case?

Answer 7.14 percent

8

Answer EMI = 2836.788Eff.Int.rate 0.962251 percent per month

Assume that in the above case the borrower defaults in the payment during the fourth yearThus, the payment goes beyond the agreed due date, upto the fifth year. What would be th

Consider a case wherein a purhaser of a Refrigerator, costing Rs.35000, pays an initial lumpurchase. He agrees to pay the rest of the money in 12 equal monthly instalments, at an int

Calculate the EMI. Also find, what is the effective rate of interest that the vendor gets at the

If a person wants to buy a house after 5 years when it is expected to cost Rs. 20 lakhs, howanually if the savings earn a compound return of 12 percent?

Shyam borrows Rs. 80,000 for a musical system at a monthly interest of 1.25%. The loan isinstalments, payable at the end of each month. Caculate the EMI.

If a person lends Rs.10,000 and receives an EMI of Rs. 2,500 annually for 6 years. What isearns on this lending?

What is the effective interest rate in the above case?


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EMI = N / [(1+r) ^ n 1 ] / [r(1+r) ^ n ]

nd pays regularly afterwards.interest rate in this case?

psum of Rs.5,000 during theerest rate of 2 percent per month.

end of the year?

much should the person save

to be repaid in 12 equal monthly

the interest rate that the person


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EMI - Solutions

1

= 2000000 / { [ (1.12^5) - 1] / 0.12}

= 314819.46

2 PVIFA r,n = [(1+r) ^ n

= 80000/ { [ (1.0125)^12-1 ] / [ 0.0125*(1.0125)^12 ] }

= 7220.665

3

6648/80000 = 8.3 percent

4 PVIFA r, 6 = 10000/2500

= 4

Find in the table the column corresponding to the PVIFA at 6 years with an approximate valuThat is at 13 %Therefore, the effective interest rate the lender gets is 13 %.

5

5000/10000 = 50 %

6 PVIFA r, 7 = 10000/2500

= 4

Find in the table the column corresponding to the PVIFA at 7 years with an approximate valu

EMI = N / [(1+r) ^ n 1 ] / [r(1+r) ^ n ]

A = FVAn / { [ (( 1+r)^n) - 1 ] / r }

The total interest earned during the period of 12 months is Rs. 6648.

(7220.665*12)-80000 = 6648This is 8.3 % of the total amount lent.

Hence, the effective monthly interest earned is, 8.3/12 , I.e., .69 percent.

This is 50 % of the total amount lent.

Hence, the effective annual interest earned is, 50 / 6 , I.e., 8.33 percent.

The total interest earned during the period of 6 years is Rs. 5000.(2500*6)-10000 = 5000

That is between 16 and 17 percent. As the value with interest 16% is nearer to 4, we can assto be around 16%.


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7

8 The actual amount due is Rs.30000.EMI = 2836.7879

The EMI therefore, is, Rs.2837.

The total interest amount paid during the period is, 0.958333

4041.4564041/35000 = 11.5%

This is 50 % of the total amount lent. Hence, the effective annual interest earned is, 50 / 7 , I.

Therefore, the effective interest rate the lender gets is 16 %.

The total interest earned during the period of 7 years is Rs. 5000.

This is 11.5 % of the total amount lent. Hence, the effective monthly interest earned is, 11.5 /

(2836.788*12)-30000 =

(2500*6)-10000 = 5000


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1 ] / [r(1+r) ^ n ]

of 4.

of 4.

me the interest rate


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., 7.14 percent.

12 , i.e., .96 %


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APR Annual Percentage Rate

For example, let's say you borrow Rs.100,000 for a 30-year mortgage loan and Lend

7%. Lender A however, will charge you Rs.2,000 in fees for the loan. Since you w

Rs.100,000, you are really only increasing your cash position by Rs.98,000 (100,00loan payments based on a Rs.100,000 loan, so your 'effective interest rate' (Annual

stated rate on your loan. In this instance the Annual Percentage Rate (APR) would

Lender B also offers a 7% interest rate, and does not charge any fees. Instead Lende

point is one percent of the loan amount, in this case 3%. Since 3% of Rs.100,000 is

cash position by Rs.97,000 (100,000 - 3,000), but would still have to repay a Rs.100

Percentage Rate (APR) would be 7.305%. In this situation Lender A has the better d

than an APR of 7.305%.


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er A is charging you an interest rate of

ould have to pay Rs.2,000 in order to get

- 2,000). However, you are still makingercentage Rate) will be higher than the

e 7.202%.

r B would require you to pay 3 points (a

Rs.3,000, you would only increase your

,000 loan. In this case your Annual

eal since an APR of 7.202% is lower

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