Compound Interest, General Mathematics

Question: The compound interest on a certain sum at `5%` per annum for `2` years is Rs.`328`.The simple interest for sum at the same rate and for the same period will be :
A
`Rs. 320`

B
`Rs. 322`

C
`Rs. 325`

D
`Rs. 326`

Note: Let the sum be.x.Then, C.I` = x (1 + 5/100)^2 - x` `= ((441x)/400 - x)` `= (41x)/400` `:. (41x/400` `= 328` `or x = (328 xx 400)/41` `= 3200` `:. S.I.Rs. ((3200 xx 5 xx 2)/100` `=Rs. 320`.
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Question: The compound interest on Rs.`5600` for `1 1/2` years at `10%` per annum, compound annumaly is :
A
`Rs. 882.70`

B
`Rs. 873.50`

C
`Rs. 868`

D
`Rs. 840`

Note: Not available
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Question: The compound interest on Rs.`20480` at `6 1/4%` per annum for `2` years `73` days is :
A
`Rs. 3000`

B
`Rs. 3131`

C
`Rs. 2929`

D
`Rs. 3636`

Note: Time`= 2 73/365` years `= 2 1/5` years :. Amount` = Rs. [ 20480 xx (1 + 25/(4 xx 100)^2 (1 + (1/5 xx 25/4)/100)]` `= Rs. (20480 xx 17/16 xx 17/16 xx 81/80)` `= Rs. 23409`. :. C.I.` Rs. (23409 - 20480)` `= Rs. 2929`.
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Question: A sum of money at compound amount which earns Rs. `578.40` in `2` years and to Rs.`614.55` in `3` years.The rate of interest per annum is :
A
`4%`

B
`5%`

C
`6 1/4%`

D
`8 1/3%`

Note: Interest on Rs.`578.40` for `1` year` = Rs.(614 - 578.40)` `=Rs. 36.15` :. Rate` = ((100 xx 36.15)/578.40)%` `= 6 1/4%`.
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Question: what is the principal amount which earns Rs.`132` as compound interest for the second year at `10%` per annum ?
A
`Rs.1000`

B
`Rs. 1200`

C
`Rs. 1320`

D
`Rs. 1188`

Note: Let the principal at the end of first year be Rs.x. Then,`(x xx 10 xx 1)/100` `= 132` `or x = 1320`. Now,let the original principal be Rs.p Then, amount after `1` year `= p + (p xx 10 xx 1)/100` `= (11p)/10`. `:. (11p)/10 = 1320` `or p = (1320 xx 10)/11` `= Rs. 1200`.
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Question: A sum of money at compound interest amounts to Rs.`5290` in `2` years and to Rs.`6083.50` in `3` years. The rate of interest per annum is :
A
`12%`

B
`14%`

C
`15%`

D
`16 2/3%`

Note: Interest on Rs.`5290` for `1` years `= Rs. (6083.50 - 5290)` `= Rs.793.50` `:. Rate = ((100 xx 793.50)/5290)%` `= 15%`.
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Question: If the amount is `2 1/4` times the sum after `2` years at compound interest ,the rate of interest per annum is :
A
`25%`

B
`30%`

C
`40%`

D
`50%`

Note: `p(1 + R/100)^2` `= 9/(4) p ⇔ (1 + R/100)^2` `= 9/4 = (3/2)^2`. `:. 1 + R/100 = 3/2` `or R/100 = 1/2` `or R = 50`.
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Question: A sum of money amounts to Rs.`4624` in`2` years and to Rs.`4913` in `3` years at compound interest. The sum is :
A
`Rs. 4096`

B
`Rs. 4260`

C
`Rs. 4335`

D
`Rs. 4360`

Note: Interest on Rs.`4624` for `1` year `= Rs. (6083.50 - 5290)` `= Rs.793.50` :.Rate `= ((100 xx 793.50)/(4624 xx 1)%` `= 6 1/4%`. Now, x `(1 + 25/(4 xx 100))^2 = 4624` `or x xx 17/16 xx 17/16 = 4624` `:.x = (46 xx 16/17 xx 16/17)` `= Rs. 4096`.
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Question: A sum of money placed at compound interest doudles itself in `5` years. It will amount to eight times itself in :
A
`10 years`

B
`12 years`

C
`15 years`

D
`20 years`

Note: `p (1 + R/100)^5` `= 2p ⇒ (1 + R/100)^5 = 2` Let `p (1 + R/100)^n` `= 8p.` Then, `(1 + R/100)^n = 8 = 2^3` `= {(1 + R/100)^5}^3` `= (1 + R/100)^15` `:. n = 15 years`.
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Question: A sum of money at compound interest amounts to thrice itself in `3` years. In how many years will it be `9` times itself ?
A
`12`

B
`9`

C
`6`

D
`8`

Note: `p (1 + R/100)^3` `= 3p ⇒ (1 + R/100)^3 = 3` Let` p(1 + R/100)^n` `= 9p ⇒ (1 + R/100)^n = 9` `:. (1 + R/100)^n = 3^2` `= [(1 + R/100)^3]^2` `= (1 + R/100)^6` Hence,n` = 6 `years.
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Question: The compound interest on a certain sum at `5%` per annum for `2` years is Rs.`328`.The simple interest for sum at the same rate and for the same period will be :

Question: The compound interest on Rs.`5600` for `1 1/2` years at `10%` per annum, compound annumaly is :

Question: The compound interest on Rs.`20480` at `6 1/4%` per annum for `2` years `73` days is :

Question: A sum of money at compound amount which earns Rs. `578.40` in `2` years and to Rs.`614.55` in `3` years.The rate of interest per annum is :

Question: what is the principal amount which earns Rs.`132` as compound interest for the second year at `10%` per annum ?

Question: A sum of money at compound interest amounts to Rs.`5290` in `2` years and to Rs.`6083.50` in `3` years. The rate of interest per annum is :

Question: If the amount is `2 1/4` times the sum after `2` years at compound interest ,the rate of interest per annum is :

Question: A sum of money amounts to Rs.`4624` in`2` years and to Rs.`4913` in `3` years at compound interest. The sum is :

Question: A sum of money placed at compound interest doudles itself in `5` years. It will amount to eight times itself in :

Question: A sum of money at compound interest amounts to thrice itself in `3` years. In how many years will it be `9` times itself ?