Question:
Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8639
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 = $8639 – $5300 = $3339
Thus, Simple Interest = $3339
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 × 3339/5300 × 9
= 333900/47700
= 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) = $5300
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3339 (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 $5300
= 9/100 × 5300
= 9 × 5300/100
= 47700/100 = 477
Thus, simple Interest for 1 year = $477
Now,
∵ If the simple Interest is $477, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/477 years
∴ If the simple Interest is $3339, then the time = 1/477 × 3339 years
= 1 × 3339/477 years
= 3339/477 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 8 years.
(3) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(4) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 7 years.
(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 3 years.
(6) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 7 years.
(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 3 years.
(10) What amount does John have to pay after 6 years if he takes a loan of $3200 at 7% simple interest?