The compound interest and simple interest on a certain sum for 2 years is
$1230 and $1200 respectively. The rate of interest is same for both compound
interest and simple interest and it is compounded annually. What is the
principle ?(without using formula).
Answers
Given that :-
C.I for 1st year is 600 and for 2nd year is 630.
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(Since it is compounded annually, S.I and C.I for 1st year would be same)
When we compare the C.I for 1st year and 2nd year, it is clear that the interest earned in 2nd year is 30 more than the first year.
Because, interest 600 earned in 1st year earned this 30 in 2nd year.
It can be considered as simple interest for one year.
That is, principal = 600, interest = 30
⇒ I = Pit
⇒ 30 = 600i(1)
⇒ 0.05 = i
⇒ 5% = i
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In the given problem, simple interest earned in two years is 1200.
⇒ I = Pit
⇒ 1200 = P x 0.05 x 2
⇒ 200 = P x 0.1
⇒ Divide both sides by 0.1.
⇒,1200/0.1 = P
⇒ 12000 = P
Hence,
⇒ The principal is $ 12,000.
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