Question:
Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9440
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 = $9440 – $5900 = $3540
Thus, Simple Interest = $3540
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 × 3540/5900 × 6
= 354000/35400
= 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) = $5900
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $3540 (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 $5900
= 6/100 × 5900
= 6 × 5900/100
= 35400/100 = 354
Thus, simple Interest for 1 year = $354
Now,
∵ If the simple Interest is $354, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/354 years
∴ If the simple Interest is $3540, then the time = 1/354 × 3540 years
= 1 × 3540/354 years
= 3540/354 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
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(2) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 8 years.
(3) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
(4) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.
(5) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
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(7) Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(9) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.
(10) Mary had to pay $3233 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.