Question:
Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 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) = 8% per annum
Amount (A) = $7396
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 = $7396 – $4300 = $3096
Thus, Simple Interest = $3096
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 × 3096/4300 × 8
= 309600/34400
= 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) = 8% per annum
Simple Interest = $3096 (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 = 8% of Principal
= 8% of $4300
= 8/100 × 4300
= 8 × 4300/100
= 34400/100 = 344
Thus, simple Interest for 1 year = $344
Now,
∵ If the simple Interest is $344, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/344 years
∴ If the simple Interest is $3096, then the time = 1/344 × 3096 years
= 1 × 3096/344 years
= 3096/344 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(2) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(3) How much loan did Mary borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6312.5 to clear it?
(4) How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?
(5) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
(6) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if James borrowed a sum of $3000 at a 10% simple interest?
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 7 years.
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 8 years.
(10) If John paid $3584 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.