CAT Previous Year Questions: Simple & Compound Interest (June 25) - CAT MCQ

“Anil invests Rs. 22000 for 6 years in a certain scheme with 4% interest per annum, compounded half-yearly.”

Total Amount of Anil’s investment after 6 years =
Let Sunil Invest a Principal of P.
“Sunil invests in the same scheme for 5 years, and then reinvests the entire amount received at the end of 5 years for one year at 10% simple interest.”
Total Amount of Sunil’s investment after 6 years = 
…the amounts received by both at the end of 6 years are same…”

Therefore, Sunil’s investment is Rs. 20808

“Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs 10,320 at the end of the first year and closes the loan by paying the outstanding amount at the end of the third year.”
This means, the amount paid by Anil at the end of the third year = (2,00,000 × 1.04² − 10,320) × 1.044 = 2,40,990.8634 ≅ 2,40,991
So the total amount paid by Anil = 10,320 + 2,40,991 = 2,51,311
So the total interest paid = 2,51,311 − 2,00,000 = 51,311

If Neetu intended to get a 5% annual interest, ideally all the banks should have maintained a 5% interest rate.
But Bank A returns 0.5% extra interest on 8000 rupees, which is 40 rupees.
But Bank B returns 0.6% extra interest on 5000 rupees, which is 30 rupees.
A & B combines are paying 70 rupees extra than 5%.
So Bank C should maintain such an interest rate that, the interest generated on the remaining 7000 rupees is 70 less than 5% interest.
Since 70 is 1% of 7000. The interest rate at Bank C should be 5% - 1% = 4%
If all the 20,000 rupees were invested in Bank C, the interest generated is 4% of 20,000 = 800 rupees.

Let the principal amount be P and the interest rate be r.
Then 

Dividing (2) by (1), we get:

r = 0.075 or 7.5%

Dividing numerator and denominator by P(1 + r)²

Raj invested Rs 10000 in the first year. Assuming the loss he faced was x%.
The amount after 1 year is 10,000 x (1 - x/100). = 10000 - 100*x.
Given the balance was greater than Rs 5000 and hence x < 50 percent.
When Raj invested this amount in the second year he earned a profit which is five times that of the first-year percentage.
Hence the amount after the second year is : 
Raj gained a total of 35 percent over the period of two years and hence the 35 percent is Rs 3500.
Hence the final amount is Rs 13,500.

Solving the equation the roots are :
x = 10, x = 70.
Since x < 50, x = 10 percent.

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
SI = 
= 40000× 0.0609 = 2436

Let after n years both the sums amount to the equal amounts. 
Then,

i.e. 
Hence 12 years after veeru invested their balances will be equal.

Let the principal be P. 

Given

⇒ P(0.1025 - 0.09) = 1125
⇒ P = 90, 000

Let the sum be P. 
Given,

⇒ 

Amount = Principal
The present value of Rs. 11,000, which is paid after 1 year, is 
The present value of Rs. 60,500, which is paid after 2 years, is 
So, borrowed amount = 10,000 + 50,000 = Rs. 60,000