Question:
Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8162
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 = $8162 – $5300 = $2862
Thus, Simple Interest = $2862
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 × 2862/5300 × 9
= 286200/47700
= 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) = $5300
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $2862 (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 $2862, then the time = 1/477 × 2862 years
= 1 × 2862/477 years
= 2862/477 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(2) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.
(3) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 7 years.
(5) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.
(6) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 3 years.
(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.
(9) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 4 years.
(10) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?