Question : A man borrowed some money and agreed to pay it off by paying Rs. 3,150 at the end of the 1st year and Rs. 4,410 at the end of 2nd year. If the rate of Compound interest is 5% per annum, then the sum is:
Option 1: Rs. 5,000
Option 2: Rs. 6,500
Option 3: Rs. 7,000
Option 4: Rs. 9,200
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Correct Answer: Rs. 7,000
Solution :
Given: $A$ = Rs. 4,410, $R$ = 5% and $t$ = 2 years
We know that $A=P(1+\frac{R}{100})^{t}$
⇒ $4410=P(1+\frac{5}{100})^{2}$
⇒ $4410=P×\frac{21}{20}×\frac{21}{20}$
⇒ $P=4410×\frac{20}{21}×\frac{20}{21}$
⇒ $P=4000$
Again, A = Rs. 3150, R = 5% and t = 1 year
⇒ $3150=P(1+\frac{5}{100})^{1}$
⇒ $3150=P×\frac{21}{20}$
⇒ $P=3150×\frac{20}{21}$
⇒ $P=3000$
$\therefore$ Total sum = 4000 + 3000 = 7000
Hence, the correct answer is Rs. 7,000.
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