Question:
Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4300
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $7310
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 = $7310 – $4300 = $3010
Thus, Simple Interest = $3010
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 × 3010/4300 × 10
= 301000/43000
= 7 years (using formula)
Thus, Time (T) = 7 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) = $4300
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $3010 (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 $4300
= 10/100 × 4300
= 10 × 4300/100
= 43000/100 = 430
Thus, simple Interest for 1 year = $430
Now,
∵ If the simple Interest is $430, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/430 years
∴ If the simple Interest is $3010, then the time = 1/430 × 3010 years
= 1 × 3010/430 years
= 3010/430 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.
(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 3% simple interest?
(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.
(4) How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?
(5) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.
(6) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.
(7) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(8) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(9) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 5% simple interest.