Question:
Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8960
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 = $8960 – $5600 = $3360
Thus, Simple Interest = $3360
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 × 3360/5600 × 6
= 336000/33600
= 10 years (using formula)
Thus, Time (T) = 10 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) = $5600
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $3360 (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 = 6% of Principal
= 6% of $5600
= 6/100 × 5600
= 6 × 5600/100
= 33600/100 = 336
Thus, simple Interest for 1 year = $336
Now,
∵ If the simple Interest is $336, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/336 years
∴ If the simple Interest is $3360, then the time = 1/336 × 3360 years
= 1 × 3360/336 years
= 3360/336 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 8 years.
(2) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.
(3) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(4) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.
(5) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 7 years.
(7) If Elizabeth paid $3864 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
(9) How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?
(10) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.