Question:
Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $4200
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7140
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 = $7140 – $4200 = $2940
Thus, Simple Interest = $2940
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 × 2940/4200 × 7
= 294000/29400
= 10 years (using formula)
Thus, Time (T) = 10 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) = $4200
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2940 (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 $4200
= 7/100 × 4200
= 7 × 4200/100
= 29400/100 = 294
Thus, simple Interest for 1 year = $294
Now,
∵ If the simple Interest is $294, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/294 years
∴ If the simple Interest is $2940, then the time = 1/294 × 2940 years
= 1 × 2940/294 years
= 2940/294 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(2) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 4 years.
(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 7 years.
(5) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?
(6) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.
(7) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?
(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 4 years.
(9) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7344 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.