Question:
Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 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) = 6% per annum
Amount (A) = $8946
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 = $8946 – $6300 = $2646
Thus, Simple Interest = $2646
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 × 2646/6300 × 6
= 264600/37800
= 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) = 6% per annum
Simple Interest = $2646 (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 $2646, then the time = 1/378 × 2646 years
= 1 × 2646/378 years
= 2646/378 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?
(2) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?
(3) Charles had to pay $4134 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?
(5) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(6) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(7) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.
(9) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?
(10) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 4% simple interest?