Question:
Margaret took a loan of $6700 at the rate of 10% 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
6
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 10% 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 × 10
= 402000/67000
= 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) = 10% 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 = 10% of Principal
= 10% of $6700
= 10/100 × 6700
= 10 × 6700/100
= 67000/100 = 670
Thus, simple Interest for 1 year = $670
Now,
∵ If the simple Interest is $670, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/670 years
∴ If the simple Interest is $4020, then the time = 1/670 × 4020 years
= 1 × 4020/670 years
= 4020/670 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 7 years.
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.
(3) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(4) Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(6) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.
(7) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 7 years.
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 7 years.
(10) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?