Question

A person earns Rs.400 on a capital of Rs.1000 as simple interest in 4 years. If the same rate of interest is applicable and compounded annually, what would be the compound interest for 2 years ?
A) Rs 210
B) Rs 310
C) Rs 100
D) Rs 200​

Answer 1

Answer:

S.I = P×T×R/100

400 = (1000×4×R)/100

400 = 40R

R = 400/40 = 10%

find the effective rate for r in the compound interest =

10%+10%+10%×10%/100 = 21

ci = 1000*21% = 210

amount = 1000*121% = rs 1210

Answer 2

Rs 210 would be the compound interest for 2 years. (Option A)

Given,

Principal Amount = P = Rs 1000

Simple Interest earned = Rs 400

Time Period = 4 years

Rate of SI = Rate of CI

Time Period for CI = 2 years

To Find,

Compound Interest for 2 years

Solution,

Simple Interest = $\frac{P*R*T}{100}$

where P is the Principal Amount

R is the Rate of Interest

T is Time Period

400 = $\frac{1000*R*4}{100}$

40000 = 4000 * R

R = 10%

Compound Interest = $P(1+\frac{R}{100} )^T - P$

Compound Interest = 1000$(1+\frac{10}{100} )^2$ - 1000

Compound Interest = 1000 (1 + 0.1)² - 1000

Compound Interest = 1000 (1.1)² - 1000

Compound Interest = 1210 - 1000

Compound Interest = 210

Thus, the interest earned is Rs 210.

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