Question:
( 1 of 10 ) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(A) 4050
(B) 4051
(C) 4052
(D) 2025.5
You selected
9
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $8236
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 = $8236 – $5800 = $2436
Thus, Simple Interest = $2436
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 × 2436/5800 × 7
= 243600/40600
= 6 years (using formula)
Thus, Time (T) = 6 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) = $5800
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2436 (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 $5800
= 7/100 × 5800
= 7 × 5800/100
= 40600/100 = 406
Thus, simple Interest for 1 year = $406
Now,
∵ If the simple Interest is $406, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/406 years
∴ If the simple Interest is $2436, then the time = 1/406 × 2436 years
= 1 × 2436/406 years
= 2436/406 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
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(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 3 years.
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(4) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
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