Question:
Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8940 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $8940
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 = $8940 – $6000 = $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 × 2940/6000 × 7
= 294000/42000
= 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) = $6000
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 $6000
= 7/100 × 6000
= 7 × 6000/100
= 42000/100 = 420
Thus, simple Interest for 1 year = $420
Now,
∵ If the simple Interest is $420, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/420 years
∴ If the simple Interest is $2940, then the time = 1/420 × 2940 years
= 1 × 2940/420 years
= 2940/420 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.
(2) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 4% simple interest?
(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 2% simple interest?
(4) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 4 years.
(6) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 3 years.
(8) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?
(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.
(10) How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?