Question:
Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6300
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9702
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 = $9702 – $6300 = $3402
Thus, Simple Interest = $3402
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 × 3402/6300 × 6
= 340200/37800
= 9 years (using formula)
Thus, Time (T) = 9 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) = 6% per annum
Simple Interest = $3402 (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 = 6% of Principal
= 6% of $6300
= 6/100 × 6300
= 6 × 6300/100
= 37800/100 = 378
Thus, simple Interest for 1 year = $378
Now,
∵ If the simple Interest is $378, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/378 years
∴ If the simple Interest is $3402, then the time = 1/378 × 3402 years
= 1 × 3402/378 years
= 3402/378 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(2) Jessica had to pay $4312.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 2% simple interest?
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 7 years.
(5) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8296 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 4 years.
(8) How much loan did Donald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7475 to clear it?
(9) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
(10) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.