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

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

(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

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

(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

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

(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

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

= 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.

= 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.

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

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

Interest & Annuity MCQ

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