Question:
Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6600
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10164
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 = $10164 – $6600 = $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 × 3564/6600 × 9
= 356400/59400
= 6 years (using formula)
Thus, Time (T) = 6 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 = $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 $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 $3564, then the time = 1/594 × 3564 years
= 1 × 3564/594 years
= 3564/594 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 4 years.
(3) How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?
(4) What amount will be due after 2 years if John borrowed a sum of $3100 at a 8% simple interest?
(5) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?
(6) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.
(7) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 7 years.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 4 years.
(10) How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?