Question:
Christopher took a loan of $6000 at the rate of 8% 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
9
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (R) = 8% 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 × 8
= 432000/48000
= 9 years (using formula)
Thus, Time (T) = 9 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) = 8% 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 = 8% of Principal
= 8% of $6000
= 8/100 × 6000
= 8 × 6000/100
= 48000/100 = 480
Thus, simple Interest for 1 year = $480
Now,
∵ If the simple Interest is $480, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/480 years
∴ If the simple Interest is $4320, then the time = 1/480 × 4320 years
= 1 × 4320/480 years
= 4320/480 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.
(2) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.
(3) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 8% simple interest?
(4) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(5) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(6) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?
(7) If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.
(9) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.
(10) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.