Question:
Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4300
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7009
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 = $7009 – $4300 = $2709
Thus, Simple Interest = $2709
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 × 2709/4300 × 7
= 270900/30100
= 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) = $4300
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2709 (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 $4300
= 7/100 × 4300
= 7 × 4300/100
= 30100/100 = 301
Thus, simple Interest for 1 year = $301
Now,
∵ If the simple Interest is $301, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/301 years
∴ If the simple Interest is $2709, then the time = 1/301 × 2709 years
= 1 × 2709/301 years
= 2709/301 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) How much loan did Barbara borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6382.5 to clear it?
(2) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.
(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 3 years.
(5) 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.
(6) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 3 years.
(7) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 4 years.
(8) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(9) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.