Question:
Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10320
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 = $10320 – $6000 = $4320
Thus, Simple Interest = $4320
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 × 4320/6000 × 9
= 432000/54000
= 8 years (using formula)
Thus, Time (T) = 8 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) = $6000
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4320 (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 = 9% of Principal
= 9% of $6000
= 9/100 × 6000
= 9 × 6000/100
= 54000/100 = 540
Thus, simple Interest for 1 year = $540
Now,
∵ If the simple Interest is $540, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/540 years
∴ If the simple Interest is $4320, then the time = 1/540 × 4320 years
= 1 × 4320/540 years
= 4320/540 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) If Mark paid $5104 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 8 years.
(3) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.
(4) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?
(5) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 4 years.
(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 6% simple interest?
(8) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(9) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.
(10) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 10% simple interest?