Question:
Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7616 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $7616
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 = $7616 – $5600 = $2016
Thus, Simple Interest = $2016
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 × 2016/5600 × 6
= 201600/33600
= 6 years (using formula)
Thus, Time (T) = 6 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 = $2016 (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 $2016, then the time = 1/336 × 2016 years
= 1 × 2016/336 years
= 2016/336 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 8 years.
(3) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 8% simple interest?
(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.
(5) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8856 to clear the loan, then find the time period of the loan.
(7) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 7% simple interest?
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 3 years.
(10) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.