Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.
Correct Answer
$8493
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 7%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5700 × 7% × 7
= $5700 ×7/100 × 7
= 5700 × 7 × 7/100
= 39900 × 7/100
= 279300/100
= $2793
Thus, Simple Interest = $2793
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $2793
= $8493
Thus, Amount to be paid = $8493 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5700
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5700 + ($5700 × 7% × 7)
= $5700 + ($5700 ×7/100 × 7)
= $5700 + (5700 × 7 × 7/100)
= $5700 + (39900 × 7/100)
= $5700 + (279300/100)
= $5700 + $2793 = $8493
Thus, Amount (A) to be paid = $8493 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5700, the simple interest in 1 year
= 7/100 × 5700
= 7 × 5700/100
= 39900/100 = $399
Thus, simple interest for 1 year = $399
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $399 × 7 = $2793
Thus, Simple Interest (SI) = $2793
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $2793
= $8493
Thus, Amount to be paid = $8493 Answer
Similar Questions
(1) If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 4 years.
(4) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 4 years.
(5) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 9% simple interest?
(6) If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(8) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?
(9) If Elizabeth paid $4140 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) How much loan did Karen borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7140 to clear it?