# Interest & Annuity  MCQ

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

(a)        Rs. 7500

(b)        Rs. 5000

(c)        Rs. 10,000

(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

(c)    Rs. 175

(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

(c)    Rs. 750

(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

(c)    Rs. 7200

(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.
$\displaystyle So,\text{ }Interest\text{ }for\text{ }3\text{ }Years\text{ }on\text{ }P12.5%=P\times \left( {\frac{{12.5}}{{100}}} \right)\times 3=\frac{{37.5\times P}}{{100}}.\text{ }So,\text{ }P+~\frac{{37.5\times P}}{{100}}=\left( {6875} \right)$
$\displaystyle So,\frac{{137.5P}}{{100}}=6875.\text{ }Or\text{ }P=\left( {\frac{{6875}}{{135.7}}} \right)\times 100=5000$
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

(c)    Rs. 1200

(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

(c)    Rs. 4200

(d)    Rs. 2300

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

(c)    Rs. 766

(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

(c)    Rs. 4

(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

(c)    Rs. 8112

(d)    Rs. 6120

$\displaystyle For\text{ }compound\text{ }interest:\text{ }A=P{{\left( {1+i} \right)}^{n}}.\text{ }Here\text{ }P=7500,\text{ }n=2,\text{ }~i=4%=\frac{4}{{100}}=0.04$
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

(c)    interest is computed annually and time is one year

(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

(c)    Rs. 156.25

(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

(c)    Rs. 10812

(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

(c)    Rs. 2000

(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

(c)    Rs. 2000

(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

(c)      Rs. 6000

(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

(c)    Rs. 91

(d)    Rs. 62

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

= 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

(c)    Rs. 1240

(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.

= 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

(c)    Rs. 3000

(d)    Rs. 4000.

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

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