Question:
Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $9540
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 = $9540 – $5300 = $4240
Thus, Simple Interest = $4240
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 × 4240/5300 × 10
= 424000/53000
= 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) = $5300
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4240 (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 = 10% of Principal
= 10% of $5300
= 10/100 × 5300
= 10 × 5300/100
= 53000/100 = 530
Thus, simple Interest for 1 year = $530
Now,
∵ If the simple Interest is $530, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/530 years
∴ If the simple Interest is $4240, then the time = 1/530 × 4240 years
= 1 × 4240/530 years
= 4240/530 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(3) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.
(4) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.
(6) If Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 7 years.
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 8 years.
(9) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.