Question:
William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $8500
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 = $8500 – $5000 = $3500
Thus, Simple Interest = $3500
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 × 3500/5000 × 7
= 350000/35000
= 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) = $5000
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3500 (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 $5000
= 7/100 × 5000
= 7 × 5000/100
= 35000/100 = 350
Thus, simple Interest for 1 year = $350
Now,
∵ If the simple Interest is $350, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/350 years
∴ If the simple Interest is $3500, then the time = 1/350 × 3500 years
= 1 × 3500/350 years
= 3500/350 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 8 years.
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.
(3) How much loan did Patricia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6180 to clear it?
(4) How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?
(5) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
(6) How much loan did Kevin borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8520 to clear it?
(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.
(9) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.
(10) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.