Question:
Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6800
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $11696
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 = $11696 – $6800 = $4896
Thus, Simple Interest = $4896
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 × 4896/6800 × 8
= 489600/54400
= 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) = $6800
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $4896 (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 $6800
= 8/100 × 6800
= 8 × 6800/100
= 54400/100 = 544
Thus, simple Interest for 1 year = $544
Now,
∵ If the simple Interest is $544, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/544 years
∴ If the simple Interest is $4896, then the time = 1/544 × 4896 years
= 1 × 4896/544 years
= 4896/544 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 4 years.
(3) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
(4) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 3 years.
(5) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 2% simple interest?
(6) If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 4 years.
(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 8 years.
(10) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 5% simple interest?