Find the compound interest on rs 50000 for one year at 8% per annum when compounded half-yearly

50000 rupees were lent for two and a half years at 8% per annum compound interest finds the compound interest at the end of 3 years.

Answer

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Hint: In this question, we will first calculate the amount from the given data of Rs.50000 at 8% compounded annually for the given period of 3years. After this, we will use the formula to calculate the compound interest.Complete step-by-step solution:
In the question, we have:
P = Rs.50000, r = 8% and t = 3 years.
We know that formula to calculate the amount at compound interest is given as:
$A = p{\left( {1 + \dfrac{r}{{100}}} \right)^t}$.................... (1)
Where A = amount obtained after 3 years
P =principal
r=rate of interest
t = Time for which money is lent.
Putting the values in equation1, we get:
$A = 50000{\left( {1 + \dfrac{8}{{100}}} \right)^3} = 50000 \times {(1.08)^3} = 62,985.6$
Therefore the amount after 3 years = $Rs.62985.6$
Now, we will use the formula to calculate the compound interest.
It is given as:
$\text{Compound interest(CI)} = \text{Amount} – \text{Principal}= A – P$
$ \Rightarrow CI = A – P$.
Putting the values in the above equation, we have:
$CI = Rs.62985.6 – Rs. 500000 = Rs.12985.6.$
Hence, the required compound interest =$ Rs.12985.6$

Note: In this type of question, we should remember the formula to calculate the amount at the given compound interest. One thing to be noted is that if the rate is given in per annum(P.a.) then take time in the year in formula and if the rate is given in per month then take time in months. This is valid for both simple interest and compound interest.

What is the difference (in Rs.) between the interests on Rs. 50,000 for one year at 8% per annum compounded half yearly and yearly?

1. 100
2. 80
3. 70
4. 50

Answer (Detailed Solution Below)

Option 2 : 80

Free

CT : General Awarensess (Mock Test)

10 Questions 10 Marks 9 Mins

Rate% for 1 year when compounded yearly = 8%

Rate% for 1 year when compounded half-yearly = [4 + 4 + (4 × 4)/100]%

⇒ 8.16%

Difference between rate percent = 8.16% - 8% = 0.16%

Difference between interest = 0.16% of 50000 = 80

∴ The required difference is Rs. 80

Alternate Method

Given:

Principal = Rs. 50,000

Rate = 8%

Formula used:

A1 = P(1 + r)t

A2 = P(1 + \(\frac{r}{{2}}\))2t

Calculation:

When interest is yearly

 A1 = P(1 + r)t

⇒ 50,000 × (1 + \(\frac{8}{{100}}\))1

⇒ (50,000 × \(\frac{108}{{100}}\))

⇒ Rs. 54,000

Now,

When interest is half-yearly

A2 = P(1 + \(\frac{r}{{2}}\))2t

⇒ 50,000 × (1 + \(\frac{8}{{200}}\))2

⇒ (50,000 × \(\frac{208}{{200}}\) × \(\frac{208}{{200}}\))

⇒ Rs. (5 × 52 × 208)

⇒ Rs. 54,080

Now,

The difference between the interests on compound half-yearly and yearly = Rs. (54,080 – 54,000)

⇒ Rs. 80

∴ The required difference is Rs. 80

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Last updated on Sep 22, 2022

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