Question:
William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $9500
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 = $9500 – $5000 = $4500
Thus, Simple Interest = $4500
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 × 4500/5000 × 10
= 450000/50000
= 9 years (using formula)
Thus, Time (T) = 9 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) = 10% per annum
Simple Interest = $4500 (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 = 10% of Principal
= 10% of $5000
= 10/100 × 5000
= 10 × 5000/100
= 50000/100 = 500
Thus, simple Interest for 1 year = $500
Now,
∵ If the simple Interest is $500, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/500 years
∴ If the simple Interest is $4500, then the time = 1/500 × 4500 years
= 1 × 4500/500 years
= 4500/500 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8932 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 8% simple interest?
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 4 years.
(4) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7602 to clear the loan, then find the time period of the loan.
(5) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(7) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 6% simple interest?
(8) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7003 to clear the loan, then find the time period of the loan.
(9) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 4% simple interest?
(10) If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.