Question:
Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $9860
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 = $9860 – $5800 = $4060
Thus, Simple Interest = $4060
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 × 4060/5800 × 10
= 406000/58000
= 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) = $5800
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4060 (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 $5800
= 10/100 × 5800
= 10 × 5800/100
= 58000/100 = 580
Thus, simple Interest for 1 year = $580
Now,
∵ If the simple Interest is $580, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/580 years
∴ If the simple Interest is $4060, then the time = 1/580 × 4060 years
= 1 × 4060/580 years
= 4060/580 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.
(3) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?
(4) How much loan did Jessica borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6325 to clear it?
(5) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.
(6) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 4% simple interest?
(8) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(9) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 2% simple interest?
(10) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.