Question:
Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8642 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) = 7% per annum
Amount (A) = $8642
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are given
Formual 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 = $8642 – $5800 = $2842
Thus, Simple Interest = $2842
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 × 2842/5800 × 7
= 284200/40600
= 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) = 7% per annum
Simple Interest = $2842 (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 $5800
= 7/100 × 5800
= 7 × 5800/100
= 40600/100 = 406
Thus, simple Interest for 1 year = $406
Now,
∵ If the simple Interest is $406, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/406 years
∴ If the simple Interest is $2842, then the time = 1/406 × 2842 years
= 1 × 2842/406 years
= 2842/406 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) How much loan did Steven borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7260 to clear it?
(2) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 4% simple interest?
(3) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 9% simple interest?
(4) If Joseph paid $4144 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?
(6) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 2% simple interest?
(7) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.
(9) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.
(10) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 to clear the loan, then find the time period of the loan.