Question:
Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9291
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 = $9291 – $5700 = $3591
Thus, Simple Interest = $3591
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 × 3591/5700 × 7
= 359100/39900
= 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) = $5700
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3591 (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 $5700
= 7/100 × 5700
= 7 × 5700/100
= 39900/100 = 399
Thus, simple Interest for 1 year = $399
Now,
∵ If the simple Interest is $399, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/399 years
∴ If the simple Interest is $3591, then the time = 1/399 × 3591 years
= 1 × 3591/399 years
= 3591/399 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(2) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 4 years.
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 7 years.
(5) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 10% simple interest?
(6) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?
(7) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
(9) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.
(10) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?