Question:
Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6900
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $11247
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 = $11247 – $6900 = $4347
Thus, Simple Interest = $4347
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 × 4347/6900 × 7
= 434700/48300
= 9 years (using formula)
Thus, Time (T) = 9 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) = $6900
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $4347 (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 $6900
= 7/100 × 6900
= 7 × 6900/100
= 48300/100 = 483
Thus, simple Interest for 1 year = $483
Now,
∵ If the simple Interest is $483, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/483 years
∴ If the simple Interest is $4347, then the time = 1/483 × 4347 years
= 1 × 4347/483 years
= 4347/483 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
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(2) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 3 years.
(4) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 7 years.
(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 4 years.
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.
(7) Daniel had to pay $4592 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 8 years.
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