Question:
Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8480
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 = $8480 – $5300 = $3180
Thus, Simple Interest = $3180
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 × 3180/5300 × 6
= 318000/31800
= 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) = $5300
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $3180 (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 = 6% of Principal
= 6% of $5300
= 6/100 × 5300
= 6 × 5300/100
= 31800/100 = 318
Thus, simple Interest for 1 year = $318
Now,
∵ If the simple Interest is $318, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/318 years
∴ If the simple Interest is $3180, then the time = 1/318 × 3180 years
= 1 × 3180/318 years
= 3180/318 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
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(2) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(4) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.
(5) If Kimberly paid $5022 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) If James borrowed $3000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.
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