Question:
Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6600
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $11352
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 = $11352 – $6600 = $4752
Thus, Simple Interest = $4752
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 × 4752/6600 × 9
= 475200/59400
= 8 years (using formula)
Thus, Time (T) = 8 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) = $6600
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4752 (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 = 9% of Principal
= 9% of $6600
= 9/100 × 6600
= 9 × 6600/100
= 59400/100 = 594
Thus, simple Interest for 1 year = $594
Now,
∵ If the simple Interest is $594, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/594 years
∴ If the simple Interest is $4752, then the time = 1/594 × 4752 years
= 1 × 4752/594 years
= 4752/594 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5440 to clear the loan, then find the time period of the loan.
(2) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 8% simple interest?
(3) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 5% simple interest?
(4) Steven had to pay $4876 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?
(6) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?
(7) How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?
(8) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.
(9) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(10) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.