Question:
Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8778
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 = $8778 – $5700 = $3078
Thus, Simple Interest = $3078
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 × 3078/5700 × 9
= 307800/51300
= 6 years (using formula)
Thus, Time (T) = 6 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) = 9% per annum
Simple Interest = $3078 (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 $5700
= 9/100 × 5700
= 9 × 5700/100
= 51300/100 = 513
Thus, simple Interest for 1 year = $513
Now,
∵ If the simple Interest is $513, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/513 years
∴ If the simple Interest is $3078, then the time = 1/513 × 3078 years
= 1 × 3078/513 years
= 3078/513 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.
(4) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(5) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?
(6) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 4 years.
(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 3 years.
(8) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(9) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8869 to clear the loan, then find the time period of the loan.