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151.

What sum will amount to Rs. 4913 in 18 months, if the rate of interest is 12 1/2% per annum, compounded half-yearly?

Answer»

Given, 

Amount = Rs.4913 

Time = 18 months \(=\frac{18}{12}\) years

\(=\frac{3}{2}\times2\) = 3 half yearly

Rate \(={12}\frac{1}{2}\text%\) \(=\frac{25}{2}\text%\)

\(=\frac{25}{4}\text%\) half yearly

Let  principal = P

So,

 \({A}={P}[({1}+\frac{R}{100})^T]\)

\(={P}({1}+\frac{25}{4\times100})^3]\) = 4913

\(={P}[(\frac{17}{16})^3]\) = 4913

\(={P}\times\frac{4913}{4096}\) 4913

\(={P}=\frac{4913\times4096}{4913}\) = Rs.4096

Hence , 

Principal = Rs. 4096
Discussion
152.

Romesh borrowed a sum of Rs. 245760 at 12.5% per annum, compounded annually. On the same day, he lent out his money to Ramu at the same rate of interest, but compounded semi-annually. Find his gain after 2 years.

Answer»

Given details are,

Principal (p) = Rs 245760

Rate (r) = 12.5% per annum

Time (t) = 2years

By using the formula,

A = P (1 + R/100) n

= 245760 (1 + 12.5/100)2

= 245760 (112.5/100)2

= Rs 311040

When compounded semi-annually,

Rate = 12.5/2% = 6.25%

Time = 2×2 years = 4years

By using the formula,

A = P (1 + R/100) n

= 245760 (1 + 6.25/100)4

= 245760 (106.25/100)4

= Rs 313203.75

∴ Romesh gain is Rs (313203.75 – 311040) = Rs 2163.75
Discussion
153.

Find the amount and the compound interest on Rs. 8000 for 1 ½ years at 10% per annum, compounded half-yearly.

Answer»

Given details are,

Principal (p) = Rs 8000

Rate (r) = 10 % per annum = 10/2% = 5% (half yearly)

Time (t) = 1 ½ years = (3/2) × 2 = 3 half years

By using the formula,

A = P (1 + R/100) n

= 8000 (1 + 5/100)3

= 8000 (105/100)3

= Rs 9261

∴ CI = Rs 9261 – 8000 = Rs 1261
Discussion
154.

A sum of ₹ 25000 was given as loan on compound interest for 3 years compounded annually at 5% per annum during the first year,6% per annum during the second year and 8% per annum during the third year. The compound interest is(a) ₹ 5035 (b) ₹ 5051 (c) ₹ 5072 (d) ₹ 5150

Answer»

(b) ₹ 5051

Explanation:

Present value= ₹ 25000

Interest rate for first year, p= 5 % per annum

Interest rate for second year, q= 6 % per annum

Interest rate for second year, r= 8 % per annum

Amount (A) = P × (1+p/100) × (1+q/100) × (1+r/100)

Now substituting the values in above formula we get,

∴ A = 25000 × (1+5/100) × (1+6/100) × (1+8/100)

⇒ A = 25000 × (105/100) × (106/100) × (108/100)

⇒ A = 21 × 53 × 27

⇒ A = ₹ 30051

∴ Compound interest = A – P

= 30051 – 25000= ₹ 5051
Discussion
155.

Find the amount and the compound interest on ₹ 2500 for 2 years at 10% per annum, compounded annually.

Answer»

Present value= ₹ 2500

Interest rate= 10% per annum

Time=2 years

To find the amount we have the formula,

Amount (A) = P (1+(R/100))n

Where P is present value, r is rate of interest, n is time in years.

Now substituting the values in above formula we get,

∴ A = 2500 (1 + 10/100)2

⇒ A = 2500 (11/10)2

⇒ A = 2500 (121/100)

⇒ A = 25 (121)

⇒ A = ₹ 3025

∴ Compound interest = A – P

= 3025 – 2500= ₹ 525
Discussion
156.

The compound interest on Rs. 4000 at 10% per annum for 2 years 3 months, compounded annually, is A. Rs. 916 B. Rs. 900 C. Rs. 961 D. Rs. 896

Answer»

Present value, P = Rs.4000 

Interest rate, R = 10% per annum 

Time, n = 2 years 3 months = (2 + 1/4) years 

∴ Amount (A) = P (1 + R/100)n × [1 + (R/4)/100] [Where, P = Present value 

R = Annual interest rate 

n = Time in years] 

∴ A = 4000 (1 + 10/100)2 × [1 + (10/4)/100] 

⇒ A = 4000 (1 + 1/10)2 × [1 + 1/40] 

⇒ A = 4000 (11/10)2 × [41/40] 

⇒ A = 4000 × 121/100 × 41/40 

⇒ A = 40 × 121 × 41/40 

⇒ A = 121 × 41 

⇒ A = 4961 

∴ Amount = Rs.4961 

∴ Compound interest = Rs.(4961 – 4000) [∵CI = A – P] 

= Rs.961
Discussion
157.

Find the amount and compound interest on   ₹ 10240 for 3 years at 12 ½ % per annum compounded annually.

Answer»

Given:

Present value= ₹ 10240

Interest rate= 12 ½ % per annum = 25/2%

Time=3 years

To find the amount we have the formula,

Amount (A) = P (1+(R/100))n

Where P is present value, r is rate of interest, n is time in years.

Now substituting the values in above formula we get,

∴ A = 10240 (1 + (25/2)/100)3

⇒ A = 10240 (1+1/8)3

⇒ A = 10240 (9/8)3

⇒ A = 31250 × 729/512 = 20 × 729

⇒ A = ₹ 14580

∴ Compound interest = A – P

= 14580 – 10240= ₹ 4340
Discussion
158.

Find the amount that David would receive if he invests Rs. 8192 for 18 months at 12 ½ % per annum, the interest being compounded half-yearly.

Answer»

Given details are,

Principal (p) = Rs 8192

Rate (r) = 12 ½ % per annum = 25/2×2 = 25/4% = 12.5/2% (half yearly)

Time (t) = 18 months = 18/12 = 1 ½ years = (3/2) ×2 = 3years

By using the formula,

A = P (1 + R/100) n

= 8192 (1 + 12.5/2×100)3

= 8192 (212.5/200)3

= Rs 9826

∴ Amount is Rs 9826.
Discussion
159.

The sum that amounts to Rs.4913 in 3 years at (25/4)% per annum compounded annually, is A. Rs. 3096 B. Rs. 4076 C. Rs. 4085 D. Rs. 4096

Answer»

Amount, A = Rs.4913 

Interest rate, R = (25/4)% per annum 

Time = 3 years 

Amount (A) = P (1 + R/100)n 

⇒ 4913 = P (1 + (25/4)/100)3 

⇒ 4913 = P (1 + 1/16)3 

⇒ 4913 = P (17/16)3 

⇒ 4913 = P × 4913/4096 

⇒ P = 4913 × 4096/4913 

⇒ P = 4096 

∴ Sum = Rs.4096
Discussion
160.

Harpreet borrowed Rs. 20000 from her friend at 12% per annum simple interest. She lent it to Alam at the same rate but compounded annually. Find her gain after 2 years.

Answer»

Present value = Rs.20000 

Interest rate = 12% per annum 

Time = 2 years 

Simple interest (SI) = PRT/100 [where, P = Present value 

R = Interest rate, T = Time] 

∴ SI = (20000 × 12 × 2)/100 

⇒ SI = 200 × 12 × 2 

⇒ SI = 4800 

Now, 

Amount (A) = P (1 + R/100)n [Where, P = Present value 

R = Annual interest rate 

n = Time in years] 

∴ A = 20000 (1 + 12/100)2 

⇒ A = 20000 (112/100)2 

⇒ A = 20000 (1.12)2 

⇒ A = 20000 × 1.2544 

⇒ A = 25088 

∴ Amount = Rs.25088 

∴ Compound interest = Rs.(25088 – 20000) 

= Rs.5088 

Now, 

(CI – SI) = 5088 - 4800 

= Rs.288 

∴ The amount of money Harpreet will gain after two years = Rs.288
Discussion
161.

The compound interest on ₹ 4000 at 10% per annum for 2 years 3 months , compounded annually, is(a) ₹ 916 (b) ₹ 900 (c) ₹ 961 (d) ₹ 896

Answer»

(c) ₹ 961

Explanation:

Present value= ₹ 4000

Interest rate= 10% per annum

Time=2 ¼ years

To find the amount we have the formula,

Amount (A) = P (1+(R/100))n

Where P is present value, r is rate of interest, n is time in years.

Now substituting the values in above formula we get,

∴ A = 4000 (1 + 10/100)2 [1 + (10/4)/100]

⇒ A = 4000 (1+1/10)2(1+ (5/2)/100)

⇒ A = 4000 (121/100) (41/40)

⇒ A = 121 × 41

⇒ A = ₹ 4961

∴ Compound interest = A – P

= 4961 – 4000= ₹ 961
Discussion
162.

Find the amount of Rs. 4096 for 18 months at 12 ½ % per annum, the interest being compounded semi-annually.

Answer»

Given details are,

Principal (p) = Rs 4096

Rate (r) = 12 ½ % per annum = 25/4% or 12.5/2%

Time (t) = 18 months = (18/12) × 2 = 3 half years

By using the formula,

A = P (1 + R/100) n

= 4096 (1 + 12.5/2×100)3

= 4096 (212.5/200)3

= Rs 4913

∴ Amount is Rs 4913
Discussion
163.

Abhay borrowed ₹ 16000 at 7 ½ % per annum simple interest. On the same day, he lent it to gurmeet at the same rate but compounded annually. What does he gain at the end of 2 years?

Answer»

Given:

Present value= ₹ 16000

Interest rate= 7 ½ % per annum= 15/2 %

Time=2 years

Now find compound interest,

To find the amount we have the formula,

Amount (A) = P (1+(R/100))n

Where P is present value, r is rate of interest, n is time in years.

Now substituting the values in above formula we get,

∴ A = 16000 (1 + (15/2)/100)2

⇒ A = 16000 (1+3/40)2

⇒ A =16000 (43/40)2

⇒ A = 16000 (1894/1600)

⇒ A = ₹ 18490

∴ Compound interest = A – P

= 18490 – 16000 = ₹ 2490

Now find the simple interest,

Simple interest (SI) = PTR/100

Where P is principle amount, T is time taken, R is rate per annum

SI = (16000 × (15/2) × 2) / 100

= 160 × 15

= ₹ 2400

Abhay gains at the end of 2 year= (CI – SI)

= 2490 – 2400

= ₹ 90
Discussion
164.

Find the amount and compound interest on ₹ 9000 for 2 years 4 months at 10 % per annum compounded annually.

Answer»

Given:

Present value= ₹ 9000

Interest rate= 10 % per annum

Time=2 years 6 months = (2 + ½) years= 5/2 years

To find the amount we have the formula,

Amount (A) = P (1+(R/100))n

Where P is present value, r is rate of interest, n is time in years.

Now substituting the values in above formula we get,

∴ A = 9000 (1 + 10/100)2 [1 + (1/3 × 10)/100]

⇒ A = 9000 (1+1/10)2 (1+1/30)

⇒ A = 9000 (11/10)2 (31/30)

⇒ A = 9000 × 121/100 × 31/30 = 9 × 121 × 31/3

⇒ A = ₹ 11253

∴ Compound interest = A – P

= 11253 – 6000 = ₹ 2253
Discussion
165.

Find the amount and compound interest on ₹ 6000 for 2 years at 9% per annum compounded annually.

Answer»

Given:

Present value= ₹ 6000

Interest rate= 9% per annum

Time=2 years

To find the amount we have the formula,

Amount (A) = P (1+(R/100))n

Where P is present value, r is rate of interest, n is time in years.

Now substituting the values in above formula we get,

∴ A = 6000 (1 + 9/100)2

⇒ A = 6000 (109/100)2

⇒ A = 6000 (1.09)2

⇒ A = 7128.6

⇒ A = ₹ 7128.6

∴ Compound interest = A – P

= 7128.6 – 6000= ₹ 1128.6
Discussion