Question:
Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 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) = 9% per annum
Amount (A) = $10318
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 = $10318 – $6700 = $3618
Thus, Simple Interest = $3618
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 × 3618/6700 × 9
= 361800/60300
= 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) = 9% per annum
Simple Interest = $3618 (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 = 9% of Principal
= 9% of $6700
= 9/100 × 6700
= 9 × 6700/100
= 60300/100 = 603
Thus, simple Interest for 1 year = $603
Now,
∵ If the simple Interest is $603, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/603 years
∴ If the simple Interest is $3618, then the time = 1/603 × 3618 years
= 1 × 3618/603 years
= 3618/603 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.
(2) What amount does John have to pay after 6 years if he takes a loan of $3200 at 8% simple interest?
(3) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
(4) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(5) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6664 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?
(7) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 4 years.
(8) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.
(10) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.