Question:
Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6300
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10269
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 = $10269 – $6300 = $3969
Thus, Simple Interest = $3969
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 × 3969/6300 × 9
= 396900/56700
= 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) = $6300
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3969 (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 $6300
= 9/100 × 6300
= 9 × 6300/100
= 56700/100 = 567
Thus, simple Interest for 1 year = $567
Now,
∵ If the simple Interest is $567, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/567 years
∴ If the simple Interest is $3969, then the time = 1/567 × 3969 years
= 1 × 3969/567 years
= 3969/567 = 7 years
Thus, time (T) = 7 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 $10332 to clear the loan, then find the time period of the loan.
(2) If Matthew paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?
(4) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.
(5) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.
(6) If Michelle paid $5544 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(8) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8688 to clear the loan, then find the time period of the loan.
(9) How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?
(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 3 years.