Question:
Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6300
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $10080
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 = $10080 – $6300 = $3780
Thus, Simple Interest = $3780
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 × 3780/6300 × 10
= 378000/63000
= 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) = $6300
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $3780 (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 $3780, then the time = 1/630 × 3780 years
= 1 × 3780/630 years
= 3780/630 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?
(2) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 8 years.
(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 8 years.
(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?
(6) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 3 years.
(9) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
(10) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 3 years.