Question:
Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6800
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $10880
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 = $10880 – $6800 = $4080
Thus, Simple Interest = $4080
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 × 4080/6800 × 6
= 408000/40800
= 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) = $6800
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $4080 (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 $6800
= 6/100 × 6800
= 6 × 6800/100
= 40800/100 = 408
Thus, simple Interest for 1 year = $408
Now,
∵ If the simple Interest is $408, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/408 years
∴ If the simple Interest is $4080, then the time = 1/408 × 4080 years
= 1 × 4080/408 years
= 4080/408 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 8% simple interest?
(3) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(4) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) If Karen paid $4424 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 after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.
(7) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12127 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.
(9) If Elizabeth paid $3726 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?