Question:
Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9690
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 = $9690 – $5700 = $3990
Thus, Simple Interest = $3990
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 × 3990/5700 × 7
= 399000/39900
= 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) = $5700
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3990 (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 $3990, then the time = 1/399 × 3990 years
= 1 × 3990/399 years
= 3990/399 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 3 years.
(2) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 9% simple interest?
(3) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.
(4) If Mary paid $3660 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 6% simple interest?
(6) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5440 to clear the loan, then find the time period of the loan.
(7) How much loan did Betty borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7812.5 to clear it?
(8) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 3 years.
(10) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.