Question:
Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9112 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9112
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 = $9112 – $6700 = $2412
Thus, Simple Interest = $2412
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 × 2412/6700 × 6
= 241200/40200
= 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) = $6700
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2412 (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 $6700
= 6/100 × 6700
= 6 × 6700/100
= 40200/100 = 402
Thus, simple Interest for 1 year = $402
Now,
∵ If the simple Interest is $402, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/402 years
∴ If the simple Interest is $2412, then the time = 1/402 × 2412 years
= 1 × 2412/402 years
= 2412/402 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?
(2) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 10% simple interest?
(3) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(4) If Nancy paid $4980 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 4 years.
(7) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.
(8) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.
(9) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 7 years.