Question:
( 3 of 10 ) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(A) 11 19/46 days or 11.413 days
(B) 22 19/46 days or 22.413 days
(C) 46 days
(D) 23 days
You selected
10.5
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9514
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 = $9514 – $6700 = $2814
Thus, Simple Interest = $2814
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 × 2814/6700 × 6
= 281400/40200
= 7 years (using formula)
Thus, Time (T) = 7 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 = $2814 (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 $2814, then the time = 1/402 × 2814 years
= 1 × 2814/402 years
= 2814/402 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Sarah had to pay $4196.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 4 years.
(3) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 9% simple interest?
(4) If Thomas paid $4256 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.
(6) If Kimberly paid $5208 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
(8) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.
(9) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(10) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.