Question:
Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $10720
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 = $10720 – $6700 = $4020
Thus, Simple Interest = $4020
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 × 4020/6700 × 6
= 402000/40200
= 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) = $6700
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $4020 (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 $4020, then the time = 1/402 × 4020 years
= 1 × 4020/402 years
= 4020/402 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?
(2) Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 3 years.
(4) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 8% simple interest?
(5) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 3% simple interest?
(6) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.
(7) If Jessica paid $4050 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(9) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
(10) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.