Sign in
Please select an account to continue using cracku.in
↓ →
The principal amount is P, rate of interest is R and time of loan is T
Formula Video
Anil invests some money at a fixed rate of interest, compounded annually. If the interests accrued during the second and third year are ₹ 806.25 and ₹ 866.72, respectively, the interest accrued, in INR, during the fourth year is nearest to
Let the principal amount be P and the interest rate be r.
Then $$P\left(1+r\right)^2-P\left(1+r\right)=806.25$$ -(1)
$$P\left(1+r\right)^3-P\left(1+r\right)^2=866.72$$ -(2)
Dividing (2) by (1), we get:
$$\frac{\left(P\left(1+r\right)^3-P\left(1+r\right)^2\right)}{P\left(1+r\right)^2-P\left(1+r\right)}=\frac{866.72}{806.25}$$
$$\frac{\left(\left(1+r\right)^2-1-r\right)}{1+r-1}=1.075$$
$$\frac{r^2+r}{r}=1.075$$
r=0.075 or 7.5%
$$\frac{\left(Interest\ accrued\ in\ 4th\ yr\right)}{Interest\ accrued\ in\ 3rd\ yr}=\frac{X}{866.72}$$
$$\frac{\left(P\left(1+r\right)^4-P\left(1+r\right)^3\right)}{P\left(1+r\right)^3-P\left(1+r\right)^2}=\frac{X}{866.72}$$
Dividing numerator and denominator by $$P\left(1+r\right)^2$$
$$\frac{r^2+2r+1-1-r}{1+r-1}=\frac{X}{866.72}$$
$$r+1=\frac{X}{866.72}$$
$$X=1.075\times\ 866.72=931.72$$
Bank A offers 6% interest rate per annum compounded half-yearly. Bank B and Bank C offer simple interest but the annual interest rate offered by Bank C is twice that of Bank B. Raju invests a certain amount in Bank B for a certain period and Rupa invests ₹ 10,000 in Bank C for twice that period. The interest that would accrue to Raju during that period is equal to the interest that would have accrued had he invested the same amount in Bank A for one year. The interest accrued, in INR, to Rupa is
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,
$$P\left(\frac{x}{100}\right)t\ =\ P\left(1+\frac{3}{100}\right)^2-P$$
$$\left(\frac{x}{100}\right)t\ =\ 1.0609-1$$
$$\left(\frac{x}{100}\right)t\ =\ 0.0609$$
We need to calculate
SI = $$10000\times\ 2t\times\ \left(\frac{2x}{100}\right)=40000\left(\frac{x}{100}\right)t=40000\times\ 0.0609=2436$$
Alex invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 years is the same as the simple interest earned on the second part at 12% per annum for 3 years. Then, the percentage of his savings invested in the first part is
Let the savings invested in first part and second part be 'x' and 'y', respectively.
It is given,
$$\ \frac{\ x\times15\times4}{100}=\ \frac{\ y\times12\times3}{100}$$
60x = 36y
5x = 3y
Required percentage = $$\frac{x}{x+y}\times100=\frac{3}{3+5}\times100=37.5\%$$
The answer is option A.
Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is
Correct Answer: 20
Let the total investment me 15x and the no. of years required be T years
$$\frac{\left(3x\times6\times T\right)}{100}+\frac{\left(5x\times10\times T\right)}{100}+\frac{\left(7x\times1\times T\right)}{100}\ge15x$$
or, $$\frac{75xT}{100}\ge15x$$
or, $$T\ge20$$
So minimum value of T is 20 years
Log in to view all questions
Login| Name | Date Taken | Score | Status |
|---|---|---|---|
| Formula Test 1 | NA | NA | |
| Formula Test 2 | NA | NA | |
| Formula Test 3 | NA | NA | |
| Formula Test 4 | NA | NA | |
| Formula Test 5 | NA | NA | |
| Formula Test 6 | NA | NA | |
| Formula Test 7 | NA | NA | |
| Formula Test 8 | NA | NA | |
| Formula Test 9 | NA | NA | |
| Formula Test 10 | NA | NA | |
| Formula Test 11 | NA | NA | |
| Formula Test 12 | NA | NA | |
| Formula Test 13 | NA | NA | |
| Formula Test 14 | NA | NA | |
| Formula Test 15 | NA | NA | |
| Formula Test 16 | NA | NA | |
| Formula Test 17 | NA | NA | |
| Formula Test 18 | NA | NA | |
| Formula Test 19 | NA | NA | |
| Formula Test 20 | NA | NA | |
| Formula Test 21 | NA | NA | |
| Formula Test 22 | NA | NA | |
| Formula Test 23 | NA | NA | |
| Formula Test 24 | NA | NA | |
| Formula Test 25 | NA | NA | |
| Formula Test 26 | NA | NA | |
| Formula Test 27 | NA | NA | |
| Formula Test 28 | NA | NA | |
| Formula Test 29 | NA | NA | |
| Formula Test 30 | NA | NA | |
| Formula Test 31 | NA | NA | |
| Formula Test 32 | NA | NA | |
| Formula Test 33 | NA | NA | |
| Formula Test 34 | NA | NA | |
| Formula Test 35 | NA | NA | |
| Formula Test 36 | NA | NA | |
| Formula Test 37 | NA | NA | |
| Formula Test 38 | NA | NA | |
| Formula Test 39 | NA | NA | |
| Formula Test 40 | NA | NA | |
| Formula Test 41 | NA | NA | |
| Formula Test 42 | NA | NA | |
| Formula Test 43 | NA | NA | |
| Formula Test 44 | NA | NA | |
| Formula Test 45 | NA | NA | |
| Formula Test 46 | NA | NA |
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Not attempted
Terms of Service
Educational materials for CAT preparation
Detailed syllabus & Topic-wise Weightage
By proceeding you agree to create your account
Free CAT Syllabus PDF will be sent to your email address soon !!!