Question:
Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6500
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $10140
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 = $10140 – $6500 = $3640
Thus, Simple Interest = $3640
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 × 3640/6500 × 7
= 364000/45500
= 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) = $6500
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3640 (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 = 7% of Principal
= 7% of $6500
= 7/100 × 6500
= 7 × 6500/100
= 45500/100 = 455
Thus, simple Interest for 1 year = $455
Now,
∵ If the simple Interest is $455, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/455 years
∴ If the simple Interest is $3640, then the time = 1/455 × 3640 years
= 1 × 3640/455 years
= 3640/455 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
(2) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(3) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(4) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.
(5) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?
(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.
(7) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.
(9) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.
(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.