Question:
John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4400
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $7964
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 = $7964 – $4400 = $3564
Thus, Simple Interest = $3564
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 × 3564/4400 × 9
= 356400/39600
= 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) = $4400
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3564 (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 $4400
= 9/100 × 4400
= 9 × 4400/100
= 39600/100 = 396
Thus, simple Interest for 1 year = $396
Now,
∵ If the simple Interest is $396, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/396 years
∴ If the simple Interest is $3564, then the time = 1/396 × 3564 years
= 1 × 3564/396 years
= 3564/396 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) How much loan did Michael borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6095 to clear it?
(2) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?
(3) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(4) How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?
(5) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(7) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.
(8) Christopher had to pay $4360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7301 to clear the loan, then find the time period of the loan.
(10) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.