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The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.

A.

Rs.18,828.80

B.

Rs.19,828.80

C.

Rs.18,028.80

D.

Rs.17,828.80

Answer with explanation

Answer: Option BExplanation

Let the sum be Rs.P

P{ [ 1 + 8/100]^{2} – 1 } = 2828.80

P(8/100)(2 + 8/100) = 2828.80 [a^{2} – b^{2} = (a – b) ( a + b)] P = 2828.80 / (0.08)(2.08) = 1360/0.08 = 17000 Principal + Interest = Rs. 19828.80

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If you can choose how frequently the interest rate on a loan is compounded that you have to pay back to someone else. In order to pay the least amount of interest would you want it rather to:

A.

compound monthly

B.

annually

C.

half-yearly

D.

it makes no difference

Answer with explanation

Answer: Option BExplanation

By compounding annually you would pay less interest than monthly compounding for example so B is the right answer.

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Find the compound interest on `25625 for 12 months at 16% per annum, compound quarterly.

A.

4352.62

B.

4252.36

C.

4562.63

D.

4456.23

Answer with explanation

Answer: Option AExplanation

Principal(P)= `25625

Rate(r) = 16% =16/4% = 4%

Time = 12 months = 4 quaters

A = 25625(1+4/100)^4 = 25625(26/25)^4= 25625×26/25×26/25×26/25×26/25=29977.62

C.I. =A-P = 29977.62-25625 = **4352.62**

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Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?

A.

3.6

B.

6

C.

18

D.

Cannot be determined

Answer with explanation

Answer: Option BExplanation

Then, [(1200×R×R)/100)]=432

→ 12R^{2}=432

→ R^{2}=36

→R=6

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An amount of $1,500 is invested for 5 years at the rates of 2% for the first two years, 5% for the third year and 6% for the fourth and fifth years all compounded continuously. What is the total amount at the end of the 5 years?

A.

$1850.51

B.

$1830.26

C.

$1930.56

D.

$200.32

Answer with explanation

Answer: Option AExplanation

A = P e ^{r t}

End of first two years: A_{ 1} = 1500 e^{ 0.02 × 2}

End of third year: A_{ 2} = A_{ 1} e^{ 0.05 × 1}

End of fifth year (last two years): A_{ 3} = A_{ 2} e^{ 0.06 × 2} = 1500 e^{ 0.02 × 2 + 0.05 × 1 + 0.06 × 2} = $1850.51

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A sum of money is invested at compound interest compounded annually. The interests in two successive years were Rs. 150 and Rs. 168. Then the rate percent was

A.

6%

B.

5%

C.

3%

D.

None of these

Answer with explanation

Answer: Option CExplanation

**Explanation:** R= (168-150)150 =12%

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Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit

A.

Rs.8820

B.

Rs.8620

C.

Rs.8520

D.

Rs.8320

Answer with explanation

Answer: Option AExplanation

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Rs.100 doubled in 5 years when compounded annually. How many more years will it take to get another Rs.200 compound interest

A.

3years

B.

5years

C.

6years

D.

7years

Answer with explanation

Answer: Option BExplanation

Rs.100 invested in compound interest becomes Rs.200 in 5 years.

The amount will double again in another 5 years.

i.e., the amount will become Rs.400 in another 5 years.

So, to earn another Rs.200 interest, it will take another 5 years.

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The difference between simple and compound interest compounded annually on a certain sum of money for 2 years at 4% per annum is re.1. the sum is

A.

625

B.

630

C.

640

D.

650

Answer with explanation

Answer: Option AExplanation

sum=Rs.x

C.I=[x(1+4/100)^2-x]=(676/625x-x)=51/625

S.I=(x*4*2)/100=2x/25

x=625

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A man invests Rs.5000 for 3 years at 5% p.a. compound interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the third year

A.

Rs.5624.32

B.

Rs.5423

C.

Rs.5634

D.

Rs.5976

Answer with explanation

Answer: Option AExplanation

5% is the rate of interest. 20% of the interest amount is paid as tax.

i.e 80% of the interest amount stays back.

if we compute the rate of interest as 80% of 5% = 4% p.a., we will get the same value.

The interest accrued for 3 years in compound interest = 3 x simple interest on principal + 3 x interest on simple interest + 1 x interest on interest on interest.

= 3 x (200) + 3 x (8) + 1 x 0.32 =600 + 24 + 0.32 = 624.32

The amount at the end of 3 years = 5000 + 624.32 = 5624.32

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A certain sum amounts to Rs.7350 in 2 years and to Rs.8575 in 3 years.find the sum and rate percent

A.

3400

B.

4400

C.

5400

D.

6400

Answer with explanation

Answer: Option CExplanation

Interest for 1 year is the same whether it’s simple interest or the compound interest.

Now interest of third year = 8575 – 7350 = 1225; means principal for this interest is 7350 if comound interest is takenIf 7350 is the principal interest = 1225

if 100 is the principal interest =(1225/7350) * 100 = 50/3 %

When a thing increases for two successive times the overall increase on initial amount = a + b + (a * b)/100

Therefore overall interest for two years = 50/3 + 50/3 + [(50/3)*(50/3)]/100 = 325/9 %

Therefore amount after 2 years = 100 + 325/9 = 1225/9

If 1225/9 is the amount principal =100

if 7350 is the amount principal =(900/1225)*7350 =5400

So sum = 5400; Rate = 50/3 %

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The compound interest on rs.30000 at 7% per annum is Rs.4347. The period is

A.

2 years

B.

2.5 years

C.

3 years

D.

4 year

Answer with explanation

Answer: Option AExplanation

Amount = Rs.(30000+4347) = Rs.34347

let the time be n years

Then,30000(1+7/100)^n = 34347

(107/100)^n = 34347/30000 = 11449/10000 = (107/100)^2

n = 2years

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If a sum on compound interest becomes three times in 4 years, then with the same interest rate, the sum will become 81 times in:

A.

12 years

B.

18 years

C.

16 years

D.

14 years

Answer with explanation

Answer: Option CExplanation

Let the sum be P

The sum P becomes 3P in 4 years on compound interest

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On a sum of money, the simple interest for 2 years is Rs. 320, while the compound interest is Rs. 340, the rate of interest being the same in both the cases. The rate of interest is

A.

15%

B.

14.25%

C.

12.5%

D.

10.5%

Answer with explanation

Answer: Option CExplanation

Simple interest for 2 years is Rs. 320

=> Simple interest for first year = 320/2 = 160

=> Similarly, simple interest for second year is also 160

Compound Interest for first year = 160

Compound Interest for second year = 340-160 = 180

we can see that compound Interest for second year is more than

simple interest for second year by 180-160 = 20

i.e., Rs.20 is the simple interest on Rs.160 for 1 year

R=100×SIPT=100×20160×1=12.5%R=100×SIPT=100×20160×1=12.5%

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A.

Rs. 10000

B.

Rs. 8000

C.

Rs. 12000

D.

Rs. 14000

Answer with explanation

Answer: Option AExplanation

Let the investment in scheme A be Rs.x

Then the investment in scheme = Rs.(15000-x)

x/10000=1=>x=10000

i.e, Amount invested in Scheme A = Rs. 10000

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