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The difference between compound interest and simple interest at the same rate on Rs 5000 for 2 years is Rs 72. The rate of interest per annum is:

A.

6%

B.

8%

C.

10%

D.

12%

Answer with explanation

Answer: Option DExplanation

Let the rate be r % p.a,

Then S. I = Rs (5000 × r/100 × 2) = Rs (100r)

C. I = Rs[5000 × (1 + r/100) ^{2} – 5000]

= Rs {5000 × [(1 + r/100) ^{2} – 1]}

= Rs [5000 × (r^{2}/2 + r/50)]

= Rs (r^{2} /2 + 100r)

(C.I) – (S.I) = (r^{2}/2 + 100r) – (100r) = r^{2}/2

Therefore, r^{2}/2 = 72

=> r^{2} = 144

=> r = 12

Hence, Rate = 12 % p.a

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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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