Question:
Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 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) = 7% per annum
Amount (A) = $6407
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 = $6407 – $4300 = $2107
Thus, Simple Interest = $2107
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 × 2107/4300 × 7
= 210700/30100
= 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) = 7% per annum
Simple Interest = $2107 (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 $2107, then the time = 1/301 × 2107 years
= 1 × 2107/301 years
= 2107/301 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 4 years.
(2) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.
(3) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
(4) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.
(5) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?
(6) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6888 to clear the loan, then find the time period of the loan.
(7) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 7 years.
(9) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?
(10) What amount will be due after 2 years if James borrowed a sum of $3000 at a 6% simple interest?