Question:
( 1 of 10 ) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
15
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6100
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $10370
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are givenFormual to Calculate Simple Interest when Principal and Amount are given
We know that, Amount (A) = Principal (P) + Simple Interest (SI)
⇒ Simple Interest (SI) = Amount – Principal
⇒ SI = $10370 – $6100 = $4270
Thus, Simple Interest = $4270
Calculation of the Time using forumula when Amount, Simple Interest and Principal are known
Formula to find the Time (T)
Time (T) = 100 × Simple Interest/Principal × Rate of Interest
⇒ T = 100 × SI/P × R
Thus, Time (T) = 100 × 4270/6100 × 7
= 427000/42700
= 10 years (using formula)
Thus, Time (T) = 10 years (from time taken before calculation)Answer
Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known
Here, we have
Principal (P) = $6100
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $4270 (As calculated above by subtracting Principal from the Amount given)
We know that, interest is calculated on the basis of the Principal.
This means Simple Interest for 1 year = Rate of simple interest × Principal
Thus, Simple Interest for 1 year = 7% of Principal
= 7% of $6100
= 7/100 × 6100
= 7 × 6100/100
= 42700/100 = 427
Thus, simple Interest for 1 year = $427
Now,
∵ If the simple Interest is $427, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/427 years
∴ If the simple Interest is $4270, then the time = 1/427 × 4270 years
= 1 × 4270/427 years
= 4270/427 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
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(4) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 5% simple interest?
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