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Compound Interest Exercise 2

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Compound Interest 2

  • This online quiz will test your knowledge of Compound Interest in Quantitative Aptitude.
  • This Online Test is useful for academic and competitive exams.
  • Multiple answer choices are given for each question in this test. You have to choose the best option.
  • After completing the test, you can see your result.
  • There is no negative marking for wrong answers.
  • There is no specified time to complete this test.

What annual payment will discharge a debt of ₹50,440 due in 3 years at 5% per annum compounded annually?

Let each instalment be ₹x. Then,

(Present worth of ₹x due 1 year hence) + Present worth of ₹x due 2 years hence) + (Present worth of ₹x due 3 years hence) = 50440

interest-33002.png

interest-32996.png

interest-32990.png

A sum of money yields at compound interest ₹200 and ₹220 at the end of first and second year respectively. The rate % is

Let Principal P = ₹x, R = r%,

C.I. = 200 at the end of Ist year

or 200 + 220 at the end of IInd year

We know that interest-32929.png

At the end of Ist year

interest-32923.png

interest-32916.png …(1)

At the end of 2nd year

interest-32910.png

interest-32904.png …(2)

On dividing (2) by (1) we get

interest-32898.png

⇒ interest-32892.png

interest-32885.png

⇒ r = 0.10 × 100

⇒ r = 10%

The compound interest accrued on an amount of ₹25,500 at the end of three year is ₹8,440.5. What would be the simple interest accrued on the same amount at the same rate in the same period?

25500 interest-36366.png– 25500 = 8440.5
⇒ interest-36360.png
= 8440.5 + 25500
⇒ interest-36354.png
interest-36348.png
= interest-36342.png
interest-36336.png
⇒ interest-36330.png
⇒ interest-36324.png
⇒ interest-36318.png
∴ Simple interest
= interest-36311.png
= ₹7650

The simple interest obtained on an amount of ₹45,000 at the end of 4 year is ₹15,300. What would be the approximate compound interest obtained on the same amount at the same rate of interest in the same period?

Rate = interest-36305.png

= 8.5%

Compound interest

= interest-36298.png– 45000

= interest-36292.png

= 45000 × 0.3858 = ₹17364 (approx)

Parameshwaran invested an amount of ₹12,000 at the simple interest rate of 10 pcpa and another amount at the simple interest rate of 20 pcpa. The total interest earned at the end of one year on the total amount invested became 14 pcpa. Find the total amount invested.

Let the second amount be ₹x. Then,

interest-36285.png

⇒ 120000 + 20 x = (12000 + x) 14

⇒ 6x = 168000 – 120000

⇒ x = ₹8000

∴ Total investment

= 12,000 + 8000 = ₹20,000

Find the difference between S.I and C.I on ₹2,000 for 2 years at the rate of 10% p.a.

For, T = 2 years

Required difference

interest-36279.png

= ₹20

The compound interest on a certain sum for 2 years is ₹41 and the simple interest is ₹40. Find the rate % p.a.

For T = 2 years,

C. I. – S. I. interest-36255.png

interest-36248.png

interest-36242.png

= ₹[21600 – (2880 + 2400 + 2000)]

= ₹14320.

What would be the simple interest, if the compound interest on the same sum for 2 years at 4% be ₹408.

For T = 2 years,

C. I. – S. I. interest-36236.png

interest-36229.png

interest-36223.png

interest-36217.png

The difference between compound interest and simple interest on a sum for 2 years at 10% per annum, when the interest is compounded annually is ₹16. If the interest were compounded half-yearly, the difference in two interests would be:

For first year, S.I. = C.I.

Now, ₹10 is S.I. on ₹100.

interest-36211.png

So, S.I. on principal for 1 year at 10% is ₹160

interest-36205.png

Amount for 2 years compounded half yearly

= interest-36199.png

∴ C.I. = ₹(1944.81 – 1600) = ₹24.81.

S.I. = interest-36193.png

∴ (C.I.) – (S.I.) = ₹(344.81 – 320) = ₹24.81.

A person lent out a certain sum on simple interest and the same sum on compound interest at certain rate of interest per annum. He noticed that the ratio between the difference of compound interest and simple interest of 3 years and that of 2 years is 25 : 8. The rate of interest per annum is:

Let the principal be ₹P and rate of interest be R% per annum.

Differecne of C.I. and S.I. for 3 years

interest-36187.png

Difference of C.I. and S.I. for 2 years

= interest-36181.png

interest-36175.png

interest-36169.png

Rahul borrowed a certain sum from Dhawan at a certain rate of simple interest for 2 years. He lent this sum to Ramesh at the same rate of interest compounded annually for the same period. At the end of two years, he received ₹4200 as compound interest but paid ₹4000 only as simple interest. Find the rate of interest.

Let the money borrowed be ₹x and the rate of interest charged = r%

Time = 2 years,

Now, 4000 = interest-36163.png

⇒ r x = 200000 ... (i)

Again, interest-36156.png

⇒ interest-36150.png

⇒ 20r + 4000 = 4200 [from (i)]

⇒ r = 10%

A person has taken a loan amount at the rate of 10 % annual compound interest and he pays that amount in two instalments of ₹968 each. How much loan did he take?

Required amount

= interest-36144.png

interest-36138.png

interest-36132.png

interest-36126.png

= interest-36120.png

interest-36114.png = ₹1680

A tree increases annually by ⅛th of its height. By how much will it increase after 2½ yearly, if it stands today 10ft high?

Increment interest-36107.png

interest-36101.png

interest-36095.png

interest-36089.png

interest-36083.png

∴ Increment in height = 13.44 – 10 = 3.44 ft

A man borrows ₹2550 to be paid back with compound interest at the rate of 4% per annum by the end of 2 years in two equal yearly instalments. How much will each instalment be?

Let the value of each instalment be ₹x. Then,

(present worth of ₹x due 1 year hence) + (present worth of ₹x due 2 years hence) = ₹2550

interest-36076.png

interest-36070.png

interest-36064.png

∴ value of each instalment = ₹1352.

Two friends A and B jointly lent out ₹81,600 at 4% per annum compound interest. After 2 years A gets the same amount as B gets after 3 years. The investment made by B was

Let A lent ₹x and B lent ₹y

Since, A and B together lent out ₹81600

∴ x + y = 81,600

Now, given (r) Rate = 4%

∴ interest-36058.png

According to the question, we have

interest-36052.png

∴ Investment made by B

= interest-36046.png

The population of a village is 10,000. If the population increases by 10% in the first year, by 20% in the second year and due to mass exodus, it decreases by 5 % in the third year, what will be its population after 3 years?

Population after 1st year

= interest-36040.png = 11000

Population after 2nd year

= interest-36034.png

Population after 3rd year

= interest-36028.png

Hence, population after 3rd year = 12,540.

A sum of money is accumulating at compound interest at a certain rate of interest. If simple interest instead of compound were reckoned, the interest for the first two years would be diminished by ₹20 and that for the first three years, by ₹61. Find the sum.

Let interest-36022.png

and I₂ = P (1+ i)t – P = P[(1+ i)t – 1]

According to the question,

20 = P [(1 + i)² – 1–2i]

and 61 = P [(1+ i)³ – 1– 3i]

On dividing, we get

interest-36016.png

interest-36010.png

interest-36004.png

As we know,

interest-35997.png

Hence, interest-35990.png20×20×20 = 8000.

A sum of money is put at compound interest for 2 years at 20% p.a. It would fetch ₹482 more, if the interest were payable half-yearly, than if it were payable yearly. Find the sum.

Let sum be ₹P. Then,

interest-32879.png … (i)

and interest-32873.png

∴ By (i), interest-32867.png

interest-32860.png

interest-32854.png

interest-32847.png

interest-32841.png

Now check your Result..

Your score is

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