Question:
William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $7700
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 = $7700 – $5000 = $2700
Thus, Simple Interest = $2700
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 × 2700/5000 × 9
= 270000/45000
= 6 years (using formula)
Thus, Time (T) = 6 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) = 9% per annum
Simple Interest = $2700 (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 = 9% of Principal
= 9% of $5000
= 9/100 × 5000
= 9 × 5000/100
= 45000/100 = 450
Thus, simple Interest for 1 year = $450
Now,
∵ If the simple Interest is $450, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/450 years
∴ If the simple Interest is $2700, then the time = 1/450 × 2700 years
= 1 × 2700/450 years
= 2700/450 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.
(2) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(3) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 10% simple interest?
(4) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 3 years.
(6) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(7) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 8 years.
(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 3 years.