Question:
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.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $11210
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 = $11210 – $5900 = $5310
Thus, Simple Interest = $5310
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 × 5310/5900 × 9
= 531000/53100
= 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) = $5900
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $5310 (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 $5900
= 9/100 × 5900
= 9 × 5900/100
= 53100/100 = 531
Thus, simple Interest for 1 year = $531
Now,
∵ If the simple Interest is $531, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/531 years
∴ If the simple Interest is $5310, then the time = 1/531 × 5310 years
= 1 × 5310/531 years
= 5310/531 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.
(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 8 years.
(4) How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?
(5) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.
(6) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?
(7) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?
(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 7 years.
(9) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 3 years.
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 3 years.