Question:
William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $7400
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 = $7400 – $5000 = $2400
Thus, Simple Interest = $2400
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 × 2400/5000 × 6
= 240000/30000
= 8 years (using formula)
Thus, Time (T) = 8 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) = $5000
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2400 (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 = 6% of Principal
= 6% of $5000
= 6/100 × 5000
= 6 × 5000/100
= 30000/100 = 300
Thus, simple Interest for 1 year = $300
Now,
∵ If the simple Interest is $300, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/300 years
∴ If the simple Interest is $2400, then the time = 1/300 × 2400 years
= 1 × 2400/300 years
= 2400/300 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?
(2) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?
(3) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.
(4) How much loan did Ashley borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7205 to clear it?
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 3 years.
(6) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 4 years.
(7) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.
(8) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.
(9) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 8% simple interest?
(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 8 years.