Test Level 1: Simple & Compound Interest - 2 - CAT MCQ

8% of 800 for 4 years + 6% of 800 for 4 years = 64 x 4 + 48 x 4 = 256 + 192 = 448. However, we do not know the rate of interest applicable in the 5th year and hence cannot determine the exact simple interest for 9 years.

Given:

Principal (P) = Rs. 10000

Time (t) = 1 year 6 months = 1.5 years

Rate of interest (r) = 10% per annum, compounded half yearly

Find compound interest (CI)

Concept:

Compound Interest = P(1 + r/n)^(nt) - P, where n is the number of times interest applied per time period.

Solution:

For half yearly compounding, n = 2 and time = 1.5 × 2 = 3 half-years

Therefore, r = 10/2 = 5% per half-year

CI = P(1 + r/n)^(nt) - P = 10000(1 + 5/100)³ - 10000

CI = 10000(1.05)³ - 10000 = Rs. 1576.25

Hence, the compound interest is Rs. 1576.25 (Option 2).

Since compounding is half yearly, it is clear that the rate of interest charged for 6 months would be 3%

Solve through options: 

For the last 5 years, the interest earned would be: 30% of 360 = 108. Thus, interest earned in the first 4 years would be ₹ 72 → ₹ 18 every year on an amount of ₹ 360- which means that the rate of interest is 5%

The annual interest would be ₹ 60. After 3 years the total value would be 1200 + 60 x 3 = 1380

2100 + 5% of 2100 = 2100 + 105 = 2205 (after 1 year). Next year it would become: 2205 + 5% of 2205 = 2205 +110.25 = 2315.25

Simple Interest for 2 years = 100 + 100 = 200.
Compound interest for 2 years: Year 1 = 5% of 2000 = 100.
Year 2: 5% of 2100 = 105 → Total compound interest = ₹ 205.
Difference between the Simple and Compound interest = 205 – 200 = ₹ 5

12500 @ 10% simple interest would give an interest of ₹ 1250 per annum. For a total interest of ₹ 5000, it would take 4 years.

8% @ 700 = ₹ 56 per year for 3 years 7.5% @ 700 = ₹ 52.5 per year for 2 years Total interest = 56 x 3 + 52.5 x 2 = 273.

Simple interest @ 23% = 4600 x 2 = 9200 Compound interest @ 20% 

→ ₹ 8800 compound interest. Difference = 9200 – 8800 = ₹ 400. 

We are given:

• Compound Interest (CI) = ₹ 420
• Rate of interest (R) = 10% per annum
• Time (T) = 2 years

The formula for Compound Interest (CI) is:

CI = P (1 +R/100)^T-P

Substituting the given values into the formula:

420 = P (1 +10/100)²-P

Simplifying:

420 = 1.21P - P

420 = P (0.21)

Finally, solve for P:

P = 4200/21

Thus, P = ₹ 2000

1331 x 1.090909 x 1.090909 x 1.090909 = 1331 x 12/11 x 12/11 x 12/11 = 1728. Hence, the rate of compound interest is 9.09%.

The value of the van would be 196000 x 6/7 x 6/7 = 144000

12% per annum compounded quarterly means that the amount would grow by 3% every 3 months.
Thus, 8000 → 8000 + 3% of 8000 = 8240 after 3 months → 8240 + 3% of 8240 = 8487.2 after 6 months and so on till five 3 month time periods get over. It can be seen that the value would turn out to be 9274.2.

He will get 20000 + 45.5% of 20000 = 29100. [Note: In this case we can take 13% simple interest compounded half yearly to mean 6.5% interest getting added every 6 months. Thus, in 42 months it would amount to 6.5 x 7 = 45.5%]

100000 + 6% of 100000 (after the first 6 months) = 106000. 
After 1 year: 106000 + 6% of 106000 = 112360 After 1 ½ years: 112360 + 6% of 112360 = 119101.6 After 2 years: 119101.6 + 6% of 119101.6 = 126247.69

The average rate of interest he pays is 186 x 100/1500 = 12.4%.
The average rate of interest being 12.4%, it means that the ratio in which the two amounts would be distributed would be 4:1 (using alligation). Thus, the borrowing at 12% would be ₹ 1200.