Interest & Annuity MCQ| Multiple Choice Questions -

Last Updated on: 13th December 2024, 12:13 pm

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Interest & Annuity MCQ

1. What principal will yield Rs. 600 as simple interest at 12% p.a in 1 year ?

(a) Rs. 7500

(b) Rs. 5000

(d) Rs. 8500

Let Principal be : P. So, 1 year Interest @12% pa= $\displaystyle \left( {\frac{{12}}{{100}}} \right)\times P=P\times \left( {\frac{3}{{25}}} \right)=\frac{{3P}}{{25}}.$
$\displaystyle So,~\frac{{3P}}{{25}}=600,\text{ }or\text{ }P=\frac{{600\times 25}}{3}=\text{ }5000.~$
So, option (b) is correct

2. What principal will yield Rs. 120 as simple interest at 6% p.a. in 10 years ?

(a) Rs. 300

(b) Rs. 225

(d) Rs. 200

Let principal be P. Simple interest @ 6% for 10 years
$\displaystyle =P\times \left( {\frac{6}{{100}}} \right)\times 10=\frac{{6P}}{{10}}.$
$\displaystyle \frac{{6P}}{{10}}=120.\text{ }So,\text{ }P=\frac{{\left( {120\times 10} \right)}}{6}=200.\text{ }$
So, option (d) is correct

3. At the rate of 6% p.a. simple interest, a sum of Rs. 2500 will earn how much interest by the end of 5 years ?

(a) Rs. 250

(b) Rs. 500

(d) Rs. 1000

Principal = 2500. Simple interest rate 6% p.a. for 5 years
$\displaystyle =2500~\times \left( {\frac{6}{{100}}} \right)=750$
So, option (c) is correct

4. Rs. 8000 becomes Rs. 10000 in two years at simple interest. The amount that will become Rs. 6875 in 3 years at the same rate of interest is

(a) Rs. 6000

(b) Rs. 5000

(d) Rs. 8250

Rs. 8000 become Rs. 10,000 in two years simple interest. So, So, Total 2 years simple interest = 10,000 – 8000 = 2000. 1 year Interest = 2000/2=1000.

So, Rate of Simple Interest= (1000 / 8000) X 100% = 12.50%. Let us assume Rs P will grow to 6875 in 3 years at same rate of interest.
So, Interest for 3 Years on P@12.5%= $\displaystyle P\times \left( {\frac{{12.5}}{{100}}} \right)\times 3=\frac{{37.5\times P}}{{100}}$
$\displaystyle So,\text{ }P+~\frac{{37.5\times P}}{{100}}=6875$
$\displaystyle So,\frac{{137.5P}}{{100}}=6875.\text{ }Or\text{ }P=\left( {\frac{{6875}}{{135.7}}} \right)\times 100=5000$
So, option (b) is correct

5. A sum was put at a certain rate of interest for 3 years. Had it been put at 2% higher rate, it would have fetched Rs. 72 more. The sum is

(a) Rs. 2250

(b) Rs. 2100

(d) Rs. 2700

Let the principal is P. Interest @2% for 3 years
$\displaystyle =P\times \left( {\frac{2}{{100}}} \right)\times 3=\frac{{6P}}{{100}}.\text{ }So,~\frac{{6P}}{{100}}=72.\text{ }So,\text{ }P=\frac{{72\times 100}}{6}=1200$
So, option (c) is correct

6. Rs. 2000 amounts to Rs. 2600 in 5 years at simple interest. If the interest rate is increased by 3 % it would amount to

(a) Rs. 2900

(b) Rs. 3700

(d) Rs. 2300

$\displaystyle Interest3\%\text{ }on\text{ }Rs.\text{ }2000\text{ }for\text{ }5\text{ }years$
$\displaystyle =2000\times \left( {\frac{3}{{100}}} \right)\times 5=300$

So, at 3% higher interest rates. 2000 amounts to (2600 + 300) = 2900. So, option (a) is correct

7. If the interest is compounded annually, the compound interest on Rs. 2000 for 3 years at 10% per annum is

(a) Rs. 481

(b) Rs. 662

(d) Rs. 601

For compound interest, A = P (1 + i)ⁿ . So, 2000 @10% pa Compound Interest for 3 years would become = 2000 X ( 1 + 0.10)³ = 2000 X (1.10)³ = 2000 x 1.331 = 2662. So, the Interest is 2662-2000 – 262. So, option (b) is correct

8. The difference between C. I. and S. I. on Rs. 2500 for 2 years at 4% p.a is

(a) Rs. 12

(b) Rs. 10

(d) Rs. 7

$\displaystyle For\text{ }compound\text{ }interest,\text{ }A=P{{\left( {1\text{ }+\text{ }i} \right)}^{n}}.\text{ }Here\text{ }~P=2500\text{ },\text{ }~n=2,\text{ }i=\frac{4}{{100}}=0.04$

So, A = 2500 (1 + 0.04)² = = 2500 (1.04)² = = 2500 x 1.0816 = 2704

Compound interest = 2704 – 2500 = 204, Simple Interest on 2500 @ 4% pa = 2500 X .04 X 2 = 200

So, Different between compound interest and simple interest = 204 – 200 = 4. So, option (c) is correct

9. The amount of Rs. 7500 at compound interest at 4% per annum for 2 years is

(a) Rs. 7300

(b) Rs. 6400

(d) Rs. 6120

$\displaystyle For\text{ }compound\text{ }interest:\text{ }A=P{{\left( {1+i} \right)}^{n}}$ .

$\displaystyle Here\text{ }P=7500,\text{ }n=2,\text{ }~i=4\%$

$\displaystyle =\frac{4}{{100}}=0.04$
So, A = 7500 (1 + 0.04)² = 7500 (1.04)² = = 7500 x 1.0816 = 8112. So, option (c) is correct

10. The simple interest is equal to compound interest for a certain sum when

(a) rate is same

(b) time is same

(d) All of above.

For Compound Interest : A = P (1 + i)ⁿ . For Simple interest A= P+ PX i = P(1+i). For n=1, for Compound Interest : A = P (1 + i)ⁿ = P(1+i). So, Simple interest and compound interest will be same for investment period of one year. So, option (c) is correct

11. The present worth of Rs. 169 due in 2 years at 4% per annum compound interest is

(a) Rs. 149

(b) Rs. 142

(d) Rs. 163

$\displaystyle For\text{ }compound\text{ }interest:\text{ }A=P{{\left( {1+i} \right)}^{n}},\text{ }Here~\text{ }A=169,$

$\displaystyle n=2\text{ },\text{ }i=4\%=\frac{4}{{100}}=0.04,\text{ }P=?$

$\displaystyle So,\text{ }169=P{{\left( {1+0.04} \right)}^{2}}.\text{ }Or\text{ }P=\frac{{169}}{{{{{\left( {1.04} \right)}}^{2}}}}=\frac{{169}}{{1.0816}}=156.25.\text{ }$
So, option (c) is correct

12. The amount of Rs. 10000.00 for 2 years at 3% will be

(a) Rs. 10609

(b) Rs. 10991

(d) Rs. 9428

For compound interest : A = P (1 + i)ⁿ. Here P = 10000, n = 2, i = 0.03, A = ?

A = 10,000 X (1 + 0.03)² = 10,000 X (1.03)² = 10,000 x 1.0609 = 10609. So, option (a) is correct

13. What will be the compound interest on Rs. 25,000 at 8% per annum for 1 years when the interest is payable half yearly?

(a) Rs. 2040

(b) Rs. 4160

(d) Rs. 3010

P = 25000, n = 2 (because interest is compound half yearly, so the period is 2 half years). $\displaystyle i=\frac{{.08}}{2}=\frac{{.04}}{{Half\text{ }Year}}\text{. }$
A = P (1 + i)ⁿ = 25,000 (1 + 0.04)² = 25,000 (1.04)² = 25,000 x 1.0816 = 27040
So, compound interest = 27040 – 25000 = 2040. So, option (a) is correct

14. What principal will amount to Rs. 2205 in 2 years at 5% per annum compound interest ?

(a) Rs. 2500

(b) Rs. 2900

(d) Rs. 2570

n = 2 i = 0.5 A = 2205 P = ?. A = P (1 + i)ⁿ = 2205 = P (1 + 0.05)². Or, 2205 = P X (1.05)²

Or, P=2205/ (1.05)²= 2205/ 1.1025 = 2000. So, option (c) is correct

15. On what principal will the compound interest for 3 years at 10% per annum amount to Rs. 993

(a) Rs. 2800

(b) Rs. 4250

(d) Rs. 3000

Compound Interest (CI) = P {(1+i/100)ⁿ -1}, where, C.I. = Compound interest, P = Principal, i = Rate of compound interest, N= Number of payment period.

So, 993=P X {1+(10/100)³-1} = P X {1.10)³ – 1} = P (1.331 – 1) = P X (0.331).
$\displaystyle So,\text{ }P=\frac{{993}}{{.331}}=3000.$
So, option (d) is correct

16. What will be the difference between the simple and compound interest on Rs. 2000 for 3 years at 10% per annum?

(a) Rs. 40

(b) Rs. 81

(d) Rs. 62

$\displaystyle Simple\text{ }Interest\text{ }SI=P\times i\times n=2000\times \left( {\frac{{10}}{{100}}} \right)\times 3=600\text{ }$

Compound Interest = P {(1+ $\displaystyle \frac{I}{{100}}$ )ⁿ -1} = 2000 X {(1+ $\displaystyle \frac{{10}}{{100}}$ )³ -1}

= 2000 {(1 + 0.10)³ – 1} = 2000 (1.331 – 1) = 2000 x 0.331 = 662
So, Difference between compound interest and simple interest = 662 – 600 = 62.
So, option (d) is correct.

17. If the simple interest on a certain sum for 3 years at 5% per annum be Rs. 1200, what would be compound interest on the same sum for the same time and same rate ?

(a) Rs. 1100

(b) Rs. 1140

(d) Rs. 1261

$\displaystyle Simple\text{ }Interest\text{ }SI=P\times i\times n=P\times \left( {\frac{5}{{100}}} \right)\times 3=\frac{{15P}}{{100}}.$
$\displaystyle So,\text{ }\frac{{15P}}{{100}}=1200.\text{ }Or\text{ }P=1200\times \frac{{100}}{{15}}=\frac{{120000}}{{15}}=8000.\text{ }$
So, Principal = 8000.

Compound Interest CI= P {(1+ $\displaystyle \frac{I}{{100}}$ )ⁿ -1} = 8000 {1 + 0.05)³ – 1} = 8000 {(1.05)³ – 1}

= 8000 (1.1576 – 1) = 8000 x (0.1576) = 1260.80 = 1261 (rounded off).
So, option (d) is correct

18. On what sum will the difference between the simple and compound interest for 2 years at 5% per annum, amount to Rs. 12.50?

(a) Rs. 4500

(b) Rs. 5000

(d) Rs. 4000.

$\displaystyle Simple\text{ }Interest\text{ }SI=P\times i\times n=P\times \left( {\frac{5}{{100}}} \right)\times 2\text{ }=\frac{P}{{10}}.$

CI= P {(1+ $\displaystyle \frac{I}{{100}}$ )ⁿ -1} = P X {(1 + 0.05)² – 1} = P X {(1.05)² – 1} = P X (1.1025 – 1) = P x (0.1025)

Now difference between CI & SI = CI-SI= .1025P – 0.1P = .025P .
So, .025P = 12.50 0r P=12.5/.025= 5000. So, option (b) is correct

19. The amount to be paid back on a loan of Rs. 18,000 at 5.5% per annum with Interest, after 3 years

a. 20970

b. 19970

c. 20370

d. 21990

Here, P=18000, R=5.5%, T=3 years

S.I. = P×R×T 100 = 18000×5.5×3 100 = Rs.2970

Amount = P + I = 18000 + 2970 = Rs. 20970

Hence Correct option is (a)

20. The difference between compound interest and simple interest on a certain amount of money at 5% per annum for 2 years is Rs.15. Find the sum

(a) Rs 4500

(b) Rs 7500

(d) Rs 6000

Let the sum be Rs. 100. Therefore, SI= $\displaystyle \frac{{100\times 5\times 2}}{{100}}$ = Rs. 10 .

On Rs. 100, CI=100 (1 + $\displaystyle \frac{5}{{100}}$ ) ² -100

= 100 ( $\displaystyle \frac{{105}}{{100}}$ ) ² -100 = 100 ( $\displaystyle \frac{{21}}{{20}}$ ) ² -100

= 100× $\displaystyle \frac{{\left( {21\times 21} \right)}}{{\left( {20\times 20} \right)}}$ − 100 = Rs. $\displaystyle \frac{{41}}{4}$

Difference of CI and SI = $\displaystyle \frac{{41}}{4}$ − 10= $\displaystyle \frac{1}{4}$

If the difference is $\displaystyle \frac{1}{4}$ , the sum = 100 . So, if the If the difference is 1 , the sum = $\displaystyle \frac{{100}}{{\left( {{1}/{4}\;} \right)}}$ =400

If the difference is Rs. 15, the sum = 400X15 =Rs.6000

Hence Correct option is (d)

21. The effective rate corresponding to a stated rate of 6% compound semiannually is approximately:

a) 6.6%

b) 6.09%

c) 6.69%

d) 5.89%

Rs. 100 at 6% compounded semiannually will become

A=100 x {1 + ( $\displaystyle \frac{{.06}}{2}$ )} ²= 100 x (1.03)² =Rs. 106.09

So, the actual amount of semi-annual compound interest is Rs 106.09 – Rs 100= Rs 6.09.

So, Rs 6.09 interest is earned on Rs 100 in 1 year with semi-annual compounding @6%.

The effective rate in % is $\displaystyle \frac{{6.09}}{{100}}$ =.0609=6.09% Thus, the effective rate is re = 6.09%

Hence Correct option is (b)

22. ₹ 60,000, was lent partly at 5% and the rest at 4% simple interest. If the total annual interest is ₹ 2560, the money lent at 4% was

(a) ₹ 40000

(b) ₹ 44000

(d) ₹ 45000

Let the amount lent at 4% be x
Therefore, Amount lent at 5% = (60000 – x )
According to the question,
{(60000−x)×5×1}/100+{(x×4×1)/100} = 2560

Or, $\displaystyle \frac{{\left( {60000-x} \right)}}{{20}}+\frac{{4x}}{{100}}$ =2560

0r, 3000- $\displaystyle \frac{x}{{20}}$ + $\displaystyle \frac{{4x}}{{100}}$ =2560

Or, 300000 – 5x + 4x=256000 (multiply both sides by 100)
or x = 300000 – 256000 = 44000

Hence Correct option is (b)

23. In how many years ₹ 3,000 would give simple interest of ₹ 1,080 at 12% per annum ?

(a) 3 years

(b) 2½ years

(d) 3½ years

We know, Time = (SI×100)/(Principal×Rate)
So, the Time in number of years = $\displaystyle \frac{{\left( {1080\times 100} \right)}}{{\left( {3000\times 12} \right)}}$

= $\displaystyle \frac{{108000}}{{36000}}=\frac{{108}}{{36}}$ = 3 years

Hence Correct option is (a)

24. P took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. P paid Rs. 432 as interest for the loan period, what was the rate of interest?

a) 3.6

b) 6

c) 18

d) 9

Here it is important to note that Interest Rate and Loan Period both are unknown. But it is given that they are equal. That means the Rate in % per annum and the Number of Years of Loan period are same. So, let us assume that the Rate is R%. The time is also R Years.

So, $\displaystyle \frac{{\left( {1200\times R\times R} \right)}}{{100}}$ = 432, or 12R² = 432, or R² = 36, or R = 6. years

Hence Correct option is (b)

25. X lent Rs. 5000 to Y for 2 years, and also lent Rs. 3000 to Z for 4 years on simple interest. The Rate of Interest is same for both Y and Z. X received Rs. Total Interest of 2200 from Y and Z. The rate of interest per annum is:

a. 5%

b. 7%

c. 9%

d. 10%

Assuming the Simple Interest Rate is R% per annum.

So, Interest from Y = $\displaystyle \frac{{\left( {5000\times R\times 2} \right)}}{{100}}$ , and Interest from Z = $\displaystyle \frac{{\left( {3000\times R\times 4} \right)}}{{100}}$ ,

So, So, {5000 x R x 2) /100} + { (3000 x R x 4) /100} = 2200.

Or, 100R + 120R = 2200, or 220R=2200. Or R= 10

Hence Correct option is (d)

26. The Ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years is :

a. 1 : 3

b. 1 : 4

c. 2 : 3

d. 3:5

Let the principal be P and Rate of interest be R%.

Then Interest for 6 years = $\displaystyle \frac{{\left( {P\times R\times 6} \right)}}{{100}}$ ., and Interest for 9 years = $\displaystyle \frac{{\left( {P\times R\times 9} \right)}}{{100}}$ .

So, the artio of Interest = {(PXRX6)/100} / {(PXRX9)/100}= $\displaystyle \frac{6}{9}=\frac{2}{3}$

So, the Ratio is 2:3

Note : Since the rat eof Interest is same, you can quickly find the ratio as per number of years, i.e 6:9 = 2:3

Hence Correct option is (c)

27. A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends the borrowed money to another person at 6.25% p.a for 2 years. Find his gain per year.

a. Rs. 112.50

b. Rs. 125

c. Rs. 225

d. Rs. 167.50

Interest paid on borrowing = $\displaystyle \frac{{\left( {5000\times 4\times 2} \right)}}{{100}}=\frac{{40000}}{{100}}$ = 400

Interest received on lending = $\displaystyle \frac{{\left( {5000\times 6.25\times 2} \right)}}{{100}}$ = $\displaystyle \frac{{62500}}{{100}}$ = 625

So, the gain in 2 years = 625-400 – 225.

So, the gain pr year = $\displaystyle \frac{{225}}{2}$ = 112.50

Hence Correct option is (a)

Interest & Annuity MCQ| Multiple Choice Questions

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