Question:
Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $11340 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) = 8% per annum
Amount (A) = $11340
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 = $11340 – $6300 = $5040
Thus, Simple Interest = $5040
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 × 5040/6300 × 8
= 504000/50400
= 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) = 8% per annum
Simple Interest = $5040 (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 = 8% of Principal
= 8% of $6300
= 8/100 × 6300
= 8 × 6300/100
= 50400/100 = 504
Thus, simple Interest for 1 year = $504
Now,
∵ If the simple Interest is $504, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/504 years
∴ If the simple Interest is $5040, then the time = 1/504 × 5040 years
= 1 × 5040/504 years
= 5040/504 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) What amount will be due after 2 years if David borrowed a sum of $3200 at a 4% simple interest?
(2) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 7 years.
(4) If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.
(7) How much loan did Michelle borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8687.5 to clear it?
(8) What amount does John have to pay after 6 years if he takes a loan of $3200 at 8% simple interest?
(9) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 2% simple interest?
(10) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.