21. The difference between the compound interest and the simple interest on Rs 28,000 for 2 years is
Rs 70 at the same rate of interest p.a.
(i) What is the rate of interest?
(ii) Calculate the interest earned in the second year under compound interest.
Answers
Answer:
5%, 1470
Step-by-step explanation:
(i)
Given: P = 28000, Time = 2 years, Difference = 70.
Let the rate of interest be R%.
⇒ [28000(1 + R/100)² - 28000] - [28000 * R * 2/100] = 70
⇒ 28000[(100 + R)²/10000 - 1 - 2R/100] = 70
⇒ 28000[(100 + R)² - 10000 - 200R/10000] = 70
⇒ 14R²/5 = 70
⇒ 14R² = 350
⇒ R² = 25
⇒ R = 5.
∴ Rate = 5%
(OR)
Difference between SI and CI = PR²/(100)²
⇒ 70 = 28000 * R²/10000
⇒ 700000 = 28000 * R²
⇒ R = 5%
Therefore, Rate = 5%
(ii)
Compound interest for the 1st year:
= (28000 * 5)/100
= 1400
Amount for the first year = 28000 + 1400 = 29400.
Compound Interest for the second year:
= (29400 * 5 * 1)/100
= 1470
Therefore, Compound Interest for the 2nd year = 1470.
Hope it helps!
SIMPLE INT. FOR EACH YR=28000xRx1/100=280R
COMPOUND INTT FOR FIRST YR=280R
70 IS THE SIMPLE INTT ON 280R FOR THE SECOND YR
280RxR/100=70
280R^2=7000
R^2=7000/280=100/4
R=UNDER ROOT 100/UNDER ROOT 4
R=10/2
R=5