Question

The difference between the simple and compound interest on a certain sum of 3 years
at 5% p.a. is Rs. 228.75. The compound interest on the sum of 2 years at 5% p.a. is
(a) Rs. 3175 (b) Rs. 3075 (c) Rs. 3275 (d) Rs. 2975

which option will be correct and why please help me ​

Answer 1

Given,

The difference between simple interest and compound interest = Rs.228.75

The time period = 3 years

The Rate of Interest = 5%

To Find,

The compound interest for 2 years.

Solution,

The formula for the difference between simple interest and compound interest of three years = $3$×$\frac{P(R^{2}) }{(100^{2}) } + P(\frac{R}{100}) ^{3}$.

Since the rate of Interest R=5, on substitution of the value of R in the formula we get

$3(\frac{P(5^{2}) }{(100^{2}) } )+ P(\frac{5}{100}) ^{3} = 0.0075P +0.000125P = 0.007625P$

Since the difference is 228.75

⇒ $0.007625P = 228.75$

⇒ $P = \frac{228.75}{0.007625}$ = $30000$

The formula for the compound Interest = $P[1+\frac{R}{100}]^{n}$, where P = Principal, R = Rate of Interest, and n = No of years

Since P = 30000, R = 5 and n = 2

On substituting the above values in the formula we get the total amount after 2 years of compound interest = $30000[1+\frac{5}{100}]^{2} = 30000(\frac{105}{100})^{2} = 33075$

Thus the interest received = $33075 - 30000 = 3075$

Henceforth, the compound interest for 2 years at 5% p.a is 3075, that is option b.

Answer 2

Answer - Correct option is b

Given,

The difference between simple interest and compound interest = $Rs.228.75$

The time period $= 3 years$

The Rate of Interest $= 5$ %

To Find - The compound interest for $2$ years.

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.

The interest, typically expressed as a percentage, can be either simple or compounded. Simple interest is based on the principal amount of a loan or deposit.

Solution,

The formula for the difference between simple interest and compound interest of three years $=3\times \frac{P(R^2)}{3\times (100^2)}+P(\frac{R}{100} )^3$

Since the rate of Interest $R=5$, on substitution of the value of R in the formula we get

$3\frac{P(5^2)}{(100^2)}+P(\frac{5}{100})^3=0.0075P+0.000125P=0.007625P$

Since the difference is $228.75$

⇒ $0.007625P=228.75$

⇒ $P=\frac{228.75}{0.007625} =30000$

The formula for the compound Interest  $=P[1+\frac{R}{100} ]^n,$ where P = Principal, R = Rate of Interest, and n = No of years

Since $P = 30000, R = 5$ and $n = 2$

On substituting the above values in the formula we get the total amount after 2 years of compound interest $= 30000[1+\frac{5}{100} ]^2=30000(\frac{105}{100} )^2=33075$

Thus, the interest received $=33075-30000=3075$

Henceforth, the compound interest for 2 years at 5% p.a is 3075, that is option b.

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