Question:
William took a loan of $5000 at the rate of 10% 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
7
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (R) = 10% 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 × 10
= 350000/50000
= 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) = $5000
Rate of Simple Interest (R) = 10% 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 = 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 $3500, then the time = 1/500 × 3500 years
= 1 × 3500/500 years
= 3500/500 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(2) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(3) How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?
(4) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
(5) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 5% simple interest?
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 7 years.
(7) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.
(8) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11800 to clear the loan, then find the time period of the loan.
(9) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 2% simple interest?
(10) If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.