Question:
Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $9412
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 = $9412 – $5200 = $4212
Thus, Simple Interest = $4212
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 × 4212/5200 × 9
= 421200/46800
= 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) = $5200
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4212 (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 = 9% of Principal
= 9% of $5200
= 9/100 × 5200
= 9 × 5200/100
= 46800/100 = 468
Thus, simple Interest for 1 year = $468
Now,
∵ If the simple Interest is $468, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/468 years
∴ If the simple Interest is $4212, then the time = 1/468 × 4212 years
= 1 × 4212/468 years
= 4212/468 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
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(2) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.
(3) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(4) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 3 years.
(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 4 years.
(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 7 years.
(8) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(9) Lisa had to pay $4414.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
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