Question:
Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $10070
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 = $10070 – $5300 = $4770
Thus, Simple Interest = $4770
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 × 4770/5300 × 10
= 477000/53000
= 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) = $5300
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4770 (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 = 10% of Principal
= 10% of $5300
= 10/100 × 5300
= 10 × 5300/100
= 53000/100 = 530
Thus, simple Interest for 1 year = $530
Now,
∵ If the simple Interest is $530, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/530 years
∴ If the simple Interest is $4770, then the time = 1/530 × 4770 years
= 1 × 4770/530 years
= 4770/530 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.
(2) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 4 years.
(3) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 8% simple interest?
(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.
(5) If Kimberly paid $5394 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 7% simple interest?
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 7 years.
(8) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 3 years.
(9) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(10) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.