Question:
Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8436
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 = $8436 – $5700 = $2736
Thus, Simple Interest = $2736
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 × 2736/5700 × 6
= 273600/34200
= 8 years (using formula)
Thus, Time (T) = 8 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) = $5700
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2736 (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 $5700
= 6/100 × 5700
= 6 × 5700/100
= 34200/100 = 342
Thus, simple Interest for 1 year = $342
Now,
∵ If the simple Interest is $342, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/342 years
∴ If the simple Interest is $2736, then the time = 1/342 × 2736 years
= 1 × 2736/342 years
= 2736/342 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
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(2) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 7 years.
(4) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
(6) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?
(7) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
(9) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(10) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.