Compound Interest
- The compound interest on ₹ 8,000 at 15% per annum for 2 years 4 months, compounded annually is:
-
View Hint View Answer Discuss in Forum
Given that , P = ₹ 8,000 , R = 15% , t = 2 years 4 months = [ 2 + ( 4 / 12 ) ] = 7 / 3 years
Using the given formula ,Amount = P 1 + R t 100 Amount = 8000 1 + 15 7/3 100 Amount = 8000 1 + 3 2 1 + 3 20 20 × 3
Correct Option: C
Given that , P = ₹ 8,000 , R = 15% , t = 2 years 4 months = [ 2 + ( 4 / 12 ) ] = 7 / 3 years
Using the given formula ,Amount = P 1 + R t 100 Amount = 8000 1 + 15 7/3 100 Amount = 8000 1 + 3 2 1 + 3 20 20 × 3 Amount = 8000 × 23 × 23 × 21 = ₹ 11109 20 20 20
∴ Compound Interest = Amount - Principal
∴ Compound Interest = ₹ (11109 – 8000) = ₹ 3109
- At what rate per annum will ₹ 32000 yield a compound interest of ₹ 5044 in 9 months interest being compounded quarterly ?
-
View Hint View Answer Discuss in Forum
Here , P = ₹ 32000 , compound interest ( CI ) = ₹ 5044 , T = 9 months = ( 3 / 4 ) years
Let the rate of CI be R percent per annum.∴ CI = P 1 + R T − 1 100 ⇒ 5044 = 32000 1 + R 3 − 1 400
[∵ Interest is compounded quarterly]⇒ 5044 = 1 + R 3 − 1 32000 400 ⇒ 1 + R 3 − 1 = 1261 400 8000 ⇒ 1 + R 3 = 1 + 1261 400 8000 ⇒ 1 + R 3 = 9261 = 21 3 400 8000 20
Correct Option: A
Here , P = ₹ 32000 , compound interest ( CI ) = ₹ 5044 , T = 9 months = ( 3 / 4 ) years
Let the rate of CI be R percent per annum.∴ CI = P 1 + R T − 1 100 ⇒ 5044 = 32000 1 + R 3 − 1 400
[∵ Interest is compounded quarterly]⇒ 5044 = 1 + R 3 − 1 32000 400 ⇒ 1 + R 3 − 1 = 1261 400 8000 ⇒ 1 + R 3 = 1 + 1261 400 8000 ⇒ 1 + R 3 = 9261 = 21 3 400 8000 20 ⇒ 1 + R = 21 ⇒ R = 21 − 1 = 1 400 20 400 20 20 ⇒ R = 400 = 20 20
- The compound interest on ₹ 2000 in 2 years if the rate of interest is 4% per annum for the first year and 3% per annum for the second year, will be
-
View Hint View Answer Discuss in Forum
Given Here , R1 = 4% , R2 = 3% , P = ₹ 2000
Using formula ,Amount = P 1 + R1 1 + R2 100 100 Amount = 2000 1 + 4 1 + 3 100 100
Correct Option: A
Given Here , R1 = 4% , R2 = 3% , P = ₹ 2000
Using formula ,Amount = P 1 + R1 1 + R2 100 100 Amount = 2000 1 + 4 1 + 3 100 100
Amount = 2000 × 1.04 × 1.03 = ₹ 2142.40
∴ CI = Amount - Principal
∴ CI = ₹ (2142.40 – 2000) = ₹ 142.40
- If the rate of interest be 4% per annum for first year, 5% per annum for second year and 6% per annum for third year, then the compound interest of ₹ 10,000 for 3 years will be
-
View Hint View Answer Discuss in Forum
Given that , R1 = 4% , R2 = 5% , R3 = 6% , P = ₹ 10,000
Using the given formula ,Amount = P 1 + R1 1 + R2 1 + R3 100 100 100 Amount = 10000 1 + 4 1 + 5 1 + 6 100 100 100
Correct Option: C
Given that , R1 = 4% , R2 = 5% , R3 = 6% , P = ₹ 10,000
Using the given formula ,Amount = P 1 + R1 1 + R2 1 + R3 100 100 100 Amount = 10000 1 + 4 1 + 5 1 + 6 100 100 100 Amount = 10000 × 26 × 21 × 53 = ₹ 11575.2 25 20 50
∴ C.I. = Amount - Principal
∴ C.I. = ₹ (11575.2 – 10000) = ₹ 1575.2
- The compound interest on ₹ 16,000 for 9 months at 20% per annum, interest being compounded quarterly, is
-
View Hint View Answer Discuss in Forum
The interest is compounded quarterly.
∴ R = 20 = 5% 4
Time = 3 quarters , P = ₹ 16,000∴ C.I. = P 1 + R T − 1 100 C.I. = 16000 1 + 5 3 − 1 100 C.I. = 16000 21 3 − 1 20
Correct Option: C
The interest is compounded quarterly.
∴ R = 20 = 5% 4
Time = 3 quarters , P = ₹ 16,000∴ C.I. = P 1 + R T − 1 100 C.I. = 16000 1 + 5 3 − 1 100 C.I. = 16000 21 3 − 1 20 C.I. = 16000 9261 − 8000 8000 C.I. = 16000 × 1261 = ₹ 2522 8000