Compound Interest, General Mathematics

Question: In how many years will a sum of Rs.`800`at `10%` per annum compounded semi - annually became Rs.`926.10 ?`
A
`2 1/2`

B
`1 1/2`

C
`2 1/3`

D
`1 1/3`

Note: Rate `= 5%` per half - year time= 2n half years = n years. Then, `800 (1 + 5/100)^2n` `= 926.10` `⇔ (21/20) = 926.10/800` `= 9261/8000` `= (21/20)^3`. `:. 2n = 3` `or n = 3/2 years`.
1. Report
Question: The present worth of Rs.`169` due in `2` years at `45` per annum compound interest is :
A
`Rs.150.50`

B
`Rs.154.75`

C
`Rs. 156.25`

D
`Rs. 158`

Note: Present worth `= Rs. [169/(1 + 4/100)]` `= Rs. (169 xx 25/26 xx 25/26)` `= Rs. 156.25`.
1. Report
Question: To find out the total compound interest accrued on a sum of money after `5` years, which of the following information given in the statements A and B is/are sufficient ? A: the rate of interest was `6%` per annum. B: The total simple interest on the same amount after `5` yaars at the same rate will be Rs.`600`
A
only A is sufficient

B
Either A or B is sufficient

C
Both A & B together are needed

D
Only A is sufficient

Note: Using A and B both, we may calculate : Sum`= ((100 xx 600)/(6 xx 5))` `= Rs. 2000`. So,the compound interest may be obtained. Thus, both A and B together are needed.
1. Report
Question: To find out the total compound interest accrued on a sum of money after `5` years, which of the folloeing informations given in the statements P and Q will be sufficient ? p: The sum was Rs.`2000` Q: The total amount of simple interest on the sum after `5` years was Rs. `4000`.
A
only P is sufficient

B
onlly Q is sufficient

C
Either P or Q is sufficient

D
Both P & Q are needed

E
Both P & Q are not sufficient

Note: Clearly, both A and Q are needed. Using P and Q, rate can be calculated as Rate`= ((100 xx 4000)/(5 xx 2000))` `= 4%` Now, C.I. can be calculated.
1. Report
Question: The difference between compound interest and the simple interest earned on a sum of money at the end of `4` years is Rs.`256.40` To find out the sum, which of the following information given in the statement P and Q is/are necessary ? p: Amount of simple interest accrued after `4` years Q: Rate of interest per annum.
A
Only P is necessary

B
only Q is necessary

C
Either P or Q is necessary

D
Neither P or Q is necessary

E
Both P and Q is necessary

Note: To find out the sum we need rate, time and the difference between C.I. and S.I. So.Q is necessary.
1. Report
Question: The difference between the compound interest and simple interest earned at the end of second year on a sum of money at `10%`per annum is Rs. `20`.The sum is :
A
`Rs.4000`

B
`Rs. 2000`

C
`Rs. 1500`

D
Date inadequate

Note: Let the principal be Rs. x. Then, C.I`= [ x (1 + 10/100)^2` S.I.`= ((x xx 10 xx 2)/100)` `= x/5` :. (C.I) - (S.I) `= ((21x)/100 - x/5)` `= x/100` `:. x/100 = 20` `or x = 2000`
1. Report
Question: A sum of Rs.`12000` deposited at compound interest becomes double after `5` years. After `20` years it will become :
A
`Rs. 120000`

B
`Rs. 192000`

C
`Rs. 124000`

D
`Rs. 96000`

Note: `12000 xx (1 + R/100)^5` `= 24000 ⇒(1 + R/100)^5 = 2` `:. [(1 + R/100)^5]^4` `= 2^4 = 16` `or (1 + R/100)^20 = 16` `or P(1 + R/100)^20 = 16p` `or 12000(1 + R/100)^20` `= 16 xx 12000` `= 192000`.
1. Report
Question: The least number of complete years in which a sum of money put out at `20%` compound interest will be more than doubled is :
A
`3`

B
`4`

C
`5`

D
`6`

Note: `P(1 + 20/100)^n> 2p or (6/5)^n > 2` Now `(6/5 xx 6/5 xx 6/5 xx 6/5) >2.` So, n = 4 years`
1. Report
Question: A tree increases annuamlly by `1/8`th of its hight. By how much will it increase after `2`years, if stands today `64` cm high ?
A
`72 cm`

B
`74 cm`

C
`75 cm`

D
`81 cm`

Note: Increase` %= (1/8 xx 100) %` `= 12 1/2%` Hight after `2` years `= [ 64 xx (1 + 25/(2 xx 100))^2] cm` `= (64 xx 9/8 xx 9/8) cm` `= 81 cm`
1. Report
Question: The difference between the compound interest and the simple interest for `2` years on a sum of money is Rs.`60`. It the simple interest for `2` years be Rs.`1440`, the rate per cent is :
A
`4 1/6%`

B
`6 1/4%`

C
`8%`

D
`8 1/3%`

Note: S.I. for `1` year = Rs.`720` S.I. on Rs.`720` for `1` year = Rs.`60` :. Rate`= ((100 xx 60)/(720 xx 1))` `= 8 1/3 %`
1. Report

First Prev 1 2 3 4 5 Next Last

Question: In how many years will a sum of Rs.`800`at `10%` per annum compounded semi - annually became Rs.`926.10 ?`

Question: The present worth of Rs.`169` due in `2` years at `45` per annum compound interest is :

Question: To find out the total compound interest accrued on a sum of money after `5` years, which of the folloeing informations given in the statements P and Q will be sufficient ? p: The sum was Rs.`2000` Q: The total amount of simple interest on the sum after `5` years was Rs. `4000`.

Question: The difference between the compound interest and simple interest earned at the end of second year on a sum of money at `10%`per annum is Rs. `20`.The sum is :

Question: A sum of Rs.`12000` deposited at compound interest becomes double after `5` years. After `20` years it will become :

Question: The least number of complete years in which a sum of money put out at `20%` compound interest will be more than doubled is :

Question: A tree increases annuamlly by `1/8`th of its hight. By how much will it increase after `2`years, if stands today `64` cm high ?

Question: The difference between the compound interest and the simple interest for `2` years on a sum of money is Rs.`60`. It the simple interest for `2` years be Rs.`1440`, the rate per cent is :