Question:
Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6300
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $12600
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 = $12600 – $6300 = $6300
Thus, Simple Interest = $6300
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 × 6300/6300 × 10
= 630000/63000
= 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) = $6300
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $6300 (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 $6300
= 10/100 × 6300
= 10 × 6300/100
= 63000/100 = 630
Thus, simple Interest for 1 year = $630
Now,
∵ If the simple Interest is $630, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/630 years
∴ If the simple Interest is $6300, then the time = 1/630 × 6300 years
= 1 × 6300/630 years
= 6300/630 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 3 years.
(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 3 years.
(3) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.
(4) If Matthew paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.
(7) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 7 years.
(9) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 4 years.