Simple & Compound Interest (February 27) - 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