At what rate percent per annum compound interest would 80000 amount to 88200 in two years?

Solution : Here the amount of principal `(P)=Rs. 80000` <br> at the rate of compound interest `(r%)=5%` in 2 years `=Rs. 80000xx(1+5/100)^(2)` <br>`=Rs 80000xx(105/100)^(2)` <br> `=Rs. 80000xx(105xx105)/(100xx100)=Rs. 88200` <br>Then after 2 years the principal `=Rs. 88200` <br> Now at the rate of 5% per annum the interest in next `1/2` year `=Rs. (88200xx5xx1)/(2xx100)=Rs. 2205` <br> `:.` The amount in `2 1/2` years `=Rs. (88200+2205)=Rs. 90405` <br> Hencce the required amount `=Rs. 90405`

Maria invested Rs 80,000 in a business. She would be paid interest at 5% per annum compounded annually. Find (i) the amount standing to her credit at the end of the second year. (ii) The interest for the third year.

Answer

Verified

Hint: Here we go through by applying the formula of amount after t year at the rate of r% compound i.e. $A = P{\left[ {1 + \dfrac{r}{{100}}} \right]^t}$ here A=amount, P=principal amount, r=rate and t=time.

Here in this question it is given that
Principal, P= Rs. 80,000
Rate of interest, r=5%
And we have to find the amount at the end of two year so t=2.
(i) The amount credited at the end of the second year, $A = P{\left[ {1 + \dfrac{r}{{100}}} \right]^t}$
Now put the values in the formula to find the amount.
$A = 80000{\left( {1 + \dfrac{5}{{100}}} \right)^2} = 80000 \times \dfrac{{21}}{{20}} \times \dfrac{{21}}{{20}} = 88200$
Hence, the amount standing to her credit at the end of the second year is Rs. 88200.

 Now for solving the (ii) part,
(ii) We have to first calculate the total amount in third year and then for finding the interest for third year we will subtract the amount of two years.
Here Principal, P= Rs. 80,000
Rate of interest, r=5%
And we have to find the amount at the end of three year so t=3.
The amount credited at the end of the third year, $A = P{\left[ {1 + \dfrac{r}{{100}}} \right]^t}$
$A = 80000{\left( {1 + \dfrac{5}{{100}}} \right)^3} = 80000 \times \dfrac{{21}}{{20}} \times \dfrac{{21}}{{20}} \times \dfrac{{21}}{{20}} = 92610$.
Interest of third year=Amount of three years-Amount of two years.
Interest=92610-88200 (as we find the amount for two years above).
=4410
$\therefore $ The interest for the third year is 44410. Answer

Note: Whenever we face such a type of question the key concept for solving the question is you must always remember the formula related to compound interest for solving such a type of question. By putting the given terms in formula you can easily get the answer. And for finding the interest for a specific year just subtract the amount of its previous year from the amount of that year.

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SSC CGL 2021 Tier-I (Held On : 11 April 2022 Shift 1)

100 Questions 200 Marks 60 Mins

GIVEN:

Principal = Rs.8000

Amount after 2 years = Rs.8820

CONCEPT:

As interest is compounded annually for 2 years, we have to square root both principal and amount and compare them to find the interest.

FORMULA USED:

Amount = Principal (1 + Rate/100)t

CALCULATION:

Let, the rate of interest be r%

Accordingly, 

8000 × (1 + r/100)2 = 8820

⇒ 8820/8000 = (1 + r/100)2

⇒ 441/400 = (1 + r/100)

⇒ 21/20 = 1 + r/100

⇒ r/100 = 1/20

⇒ r = 5

∴ Rate of Interest is 5%  per annum.

Last updated on Oct 8, 2022

The SSC CGL 2022 application date date extended till 13th October 2022. The SSC CGL Notification was out on 17th September 2022. The SSC CGL Eligibility will be a bachelor’s degree in the concerned discipline. This year, SSC has completely changed the exam pattern and for the same, the candidates must refer to SSC CGL New Exam Pattern.

Let's discuss the concepts related to Interest and Compound Interest. Explore more from Quantitative Aptitude here. Learn now!

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• Compound Interest Exercise 2.1
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ML Aggarwal Solutions Class 9 Mathematics Solutions for Compound Interest Exercise 2.2 in Chapter 2 - Compound Interest

Question 20 Compound Interest Exercise 2.2

At what rate percent p.a. compound interest would ₹ 80000 amounts to ₹ 88200 in two years, interest

being compounded yearly. Also, find the amount after 3 years at the above rate of compound interest.

Answer:

It is given that

Principal (P) = ₹ 80000

Amount (A) = ₹ 88200

Period (n) = 2 years

Consider r% per annum as the rate of interest percent

We know that

So we get

1 + r/100 = 21/20

r/100 = 21/20 – 1 = 1/20

By cross multiplication

r = 1/20 × 100 = 5

Hence, the rate of interest is 5% per annum.

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