In what time will rupees 6250 amount to rupees 6760 at 8% per annum if the interest is compounded half yearly?

Present value = Rs.6250

Interest rate = 8 % per annum

Time = 1 years

∵ Interest is compounded half-yearly.

∴ Amount (A) = P [1 + (R/2)/100]2n [Where, P = Present value

R = Annual interest rate

n = Time in years]

∴ A = 6250 [1 + (8/2)/100]2

⇒ A = 6250 [1 + 4/100]2

⇒ A = 6250 [26/25]2

⇒ A = 6250 × 26/25 × 26/25

⇒ A = 10 × 26 × 26

⇒ A = 6760

∴ Amount = Rs.6760

∴ Compound interest = Rs.(6760 – 6250)

= Rs.510

∴ Divakaran gets a CI of Rs.510.

• question_answer A certain sum invested with interest of 8% per annum, compounded semi-annually amounts to Rs. 6760 at the end of 1 yr. The sum is                                                                                             [SSC (CPO) 2014] A) Rs. 6000                        B) Rs. 6520 C) Rs. 6250            (adsbygoogle = window.adsbygoogle || []).push({}); D) Rs. 6500

  Correct Answer: C

  Solution :

  Let the sum invested be Rs. x.

  Amount at the end of 1 yr = Rs. 6760

  Now, rate of interest = 8% and time duration is 1 yr.

  Given, in the question that the amount is compounded semi-annually, i.e. half-yearly.

  Hence, rate of interest changes to

  \[\frac{R}{2}=\frac{8}{2}\]% =4%

  and time duration becomes \[2t=2\times 1=2\,\,yr\]

  By the formula of compound interest, we get

  Amount \[=P{{\left( 1+\frac{R}{100} \right)}^{t}}\]

  \[\Rightarrow \]\[6760=x{{\left( 1+\frac{4}{100} \right)}^{2}}\]\[\Rightarrow \]\[x=\frac{6760}{{{\left( 1+\frac{1}{25} \right)}^{2}}}\]

  \[\Rightarrow \]   \[x=\frac{6760\times 25\times 25}{26\times 26}=10\times 25\times 25\]

  \[\Rightarrow \]   \[x=6250\]

1. Calculate the simple interest if P = Rs. 4800,   T = 2 years,   R = 8 %?

Sol:
P = 4800Rs,   T = 2 years,   R = 8 % .....(Given)

2. Find the simple interest on Rs. 6250 at 4 % per annum for the period from December 27,2002 to May 22, 2003. Also find the amount ?

Sol:
Given
Principal (P) = Rs. 6250, Rate (R) = 4%,
Time (T) = December 27, 2002 to May 22, 2003
The number of days per which the money was kept may be counted as :

3. At what rate percent per annum will the amount Rs.72 produce an interest of Rs. 115.20 in 2 years?

Sol:
Given that the principal amount (P) = Rs.72, time(T) = 2 years.
The Simple interest (SI) = Rs.115.20
Now we have to calculate the rate per cent at which the Rs.72 will
produce a simple interest of Rs.115.20
We know that SI = PTR/100

4. If Rs.1250 amount to Rs.1550 in 3 years at simple interest, then find the rate of percentage?

Sol :
Given
Principal amount (P) = 1250 Rs, Time(T) = 3 years
Total amount (A) = Rs.1550

5. Calculate the simple interest and compound interest if principal = Rs. 6000
Rate = 10% and time period = 2 years ?

6. Find the compound interest on Rs. 8000 at 5% per annum, for 2 years, compounded annually ?

Sol:
Given

7. What is the amount to be paid on a loan of Rs. 62500 for 3/2 years at 8 % per annum, compounded half – yearly?

Sol: Given,

What is the compound interest on Rs 6250 at 8% per annum for 1 year if compounded half yearly?

In what time will ₹ 6250 amount to ₹ 6632.55 at 4% compound interest payable half yearly?

What would be compound interest of an amount 6250?