Test: Compound Interest- 1 - CAT MCQ

Simple interest = P * r * t /100, where, P is the Principal, r is the rate of interest and t is the time period such that the rate of interest and the time period have mutually compatible units like r % per annum and t years.

Here, in the first case, let the Principal be Rs.P and rate of interest be r % per annum. Time period is given as 8 years . Interest is given as 80 P / 100
So, 80 P / 100 = P * r * 8 / 100
Or, 80 = 8 r
So, r = 10 % per annum.

Now, in the second case, Principal is given as Rs. 14,000, rate of compound interest is 10 % per annum as determined above; and t is 3 years.
Compound interest = P * ( 1 + r/100)t - P 
= 14,000 * ( 1+ 10 /100)3 - 14,000
= 14,000 * ( 1 + 0.1)3 - 14,000
= 14,000 *(1.1)3 - 14,000
(14,000 * 1.331) - 14,000
= 18,634 - 14,000 = 4,634
So, the compound interest on Rs.14,000 at the same rate of interest as in case 1 in 3 years will be Rs. 4,634.

Amount = Rs.(30000+4347) = Rs.34347
let the time be n years
Then,30000(1+7/100)ⁿ = 34347
(107/100)ⁿ = 34347/30000 
= 11449/10000 
= (107/100)²
n = 2years

[15000×(1+R/100)² − 15000] - (15000×R×2)/100 = 96
⇒15000[(1+R/100)² − 1 − 2R/100]=96
⇒ 15000[(100+R)² − 10000−(200×R)]/10000 = 96
⇒ R2 = (96×23) = 64
⇒ R = 8
∴ Rate = 8%

Amount after 3 years = P(1 + R/100)^T
=> 40000(1 + 11/100)³
=> 40000(111/100)³
=> 40000[(111*111*111)/(100*100*100)]
=> (4*111*111*111)/100 
=> 54705.24
Compound Interest = 54705.24 - 40000 
= Rs. 14705.24

Let the rate be R% per annum
P(1+R/100)T = 1573.04
= 1400(1+R/100)2 = 1573.04
= (1+R/100)2 = 1573.04/1400 = 157304/140000 = 11236/10000
(1+R/100) = (√11236/10000)
= (√11236)/(√10000)
= 106/100
R/100 = (106/100 − 1)
=> 6/100
R = 6%

It is given that Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. It is also
known that he repays Rs 10320 at the end of the first year and closes the loan by paying the outstanding
amount at the end of the third year.

The total amount at the end of the first year is: 200000 x 104/100 x 104/100 = 216320

He repays 10320 rupees at the end of the first year, which implies the amount that remains unpaid at the end of
the first year is 206000 rupees.

This unpaid amount will accrue interest for another two years.

Hence, the final amount at the end of three years is 206000 x 104/100 x 104/100 x 104/100 x 104/100 = 240990.86

Hence, the accrued interest in these two years is (240990.86-206000) = 34990.86 rupees.

Hence, the total interest accrued over the three years = (34990.86+16320) = 51311 rupees.

Bank A: 6% p.a. 1/2 yearly (CI)

Bank B: x% p.a (SI)

Bank C: 2x% p.a (SI)

Let Raju invest Rs P in bank B for t years. Hence, Rupa invests Rs 10,000 in bank C for 2t years.
Now, 

We need to calculate