At what percent per annum will 5000 amount to 5832 in 2 years compounded annually?

1. Percent:

(i) Percent means per hundred or for every hundred.

(ii) A fraction with its denominator as 100 is called a percent and is equal to that percent as is the numerator.

(iii) A ratio with its second term 100 is also called a percent.

2. Converting to Percent:

(i) To convert a fraction into a percent, we multiply the fraction by 100.

(ii) To convert a ratio into a percent, we write it as a fraction and multiply it by 100.

(iii) To convert a decimal into a percent, we shift the decimal point two places to the right.

3. Converting from Percent:

(i) To convert a percent into a fraction, we drop percent sign (%) and divide the remainder by 100.

(ii) To convert a percent into a ratio, we drop percent sign (%) and form a ratio with the remaining number as the first term and 100 as the second term.

(iii) To convert a percent into a decimal, we drop percent sign (%) and shift the decimal point two places to the left.

4. Increase Per cent of a Value:

Increase% = Increase in valueOriginal value×100%

5. Decrease Per cent of a Value:

Decrease %=Decrease in valueOriginal value×100%

6. Profit:

(i) Profit=S.P.-C.P.

(ii) Profit %=Profit C.P. ×100 or Profit= C. P. × Profit %100 

(iii) S.P.=C.P.100+ Profit%100 

(iv) C.P.=100×S.P.(100+ Profit%)

7. Loss:

(i) Loss=C.P.-S.P.

(ii) Loss %=Loss C.P.×100 or Loss=C.P. ×L oss %100 

(iii) S.P.=C.P.100-Loss %100 

(iv) C.P.=100×S.P.100-Loss %

8. Discount:

(i) Discount=M.P.-S.P.

(ii) Rate of Discount=Discount %= Discount M.P.×100

(iii) S.P.=M.P.100-Discount % 100

(iv) M.P.=100×S.P.(100-Discount %)

9. Value added tax (VAT) is charged on the selling price of an article.

10. If the borrower and the lender agree to fix up a certain interval of time (say, a year or a half-year or a quarter of a year etc.) so that the amount at the end of an interval becomes the principal for the next interval, then the total interest over all the intervals calculated in this way is called the compound interest and is denoted by C.I. Also, C.I.=Amount−Principal.

11. Compound Interest:

(i) Let P be the principal and the rate of interest be R%   per annum. If the interest is compounded annually, then the amount A and the compound interest C.I. at the end of n years are given by

A=P1+R100n and, C.I.=A-P=P1+R100n-1  respectively.

(ii) Let P be the principal and the rate of interest be R1% for first year, R1% for second year, R1% for third year and so on and in last Rn% for the nth year. Then, the amount A  and the compound interest C.I. at the end of n years are given by

A=P1+R11001+R2100…1+Rn100  and, C.I.=A-P respectively.

(iii) Let P be the principal and the rate of interest be R% per annum. If the interest is compounded annually but time is the fraction of a year, say 514 years, then amount A is given by

A=P1+R11005 1+R4100 and, C.I.=A-P

12. Population Growth:

(i) Let P be the population of a city or town at the beginning of a certain year and the population grows at a constant rate of R% per annum, then

Population after n years=P1+R100n

(ii) Let P be the population of a city or a town at the beginning of a certain year. If the population grows at the rate of R1% during first year and R2% during second year, then 

Population after 2 years=P1+R1100×1 +R2100.

Present value, P = Rs.5000

Amount, A = Rs.5832

Time, n = 2 years

Now,

Amount (A) = P (1 + R/100)n [Where, A = Amount with compound interest

P = Present value

R = Annual interest rate

n = Time in years]

∴ Amount (A) = P (1 + R/100)n

⇒ 5832 = 5000 (1 + R/100)2

⇒ (1 + R/100)2 = 5832/5000

⇒ (1 + R/100)2 = 2916/2500

⇒ (1 + R/100)2 = (54/50)2

⇒ 1 + R/100 = 54/50

⇒ R/100 = (54/50) - 1

⇒ R/100 = (54 – 50)/50

⇒ R/100 = 4/50

⇒ R = 400/50

⇒ R = 8

∴ Rate = 8 %.

At what rate percent annum will 5000 amount to 5832 in 2 years compounded annually?

At what rate compound interest per annum will 5000 amount to 5618 in 2 years?

What will be the compound interest on 5000 in 2 years?

At what rate of compound interest will Rs 5000 become Rs 5408 after 2 years?