Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 7 years.
Correct Answer
$9291
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 9%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 7
= $5700 ×9/100 × 7
= 5700 × 9 × 7/100
= 51300 × 7/100
= 359100/100
= $3591
Thus, Simple Interest = $3591
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 + $3591
= $9291
Thus, Amount to be paid = $9291 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) = 9%
And, Time (t) = 7 years
Thus, Amount (A)
= $5700 + ($5700 × 9% × 7)
= $5700 + ($5700 ×9/100 × 7)
= $5700 + (5700 × 9 × 7/100)
= $5700 + (51300 × 7/100)
= $5700 + (359100/100)
= $5700 + $3591 = $9291
Thus, Amount (A) to be paid = $9291 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5700, the simple interest in 1 year
= 9/100 × 5700
= 9 × 5700/100
= 51300/100 = $513
Thus, simple interest for 1 year = $513
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $513 × 7 = $3591
Thus, Simple Interest (SI) = $3591
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $3591
= $9291
Thus, Amount to be paid = $9291 Answer
Similar Questions
(1) Kimberly had to pay $5208 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?
(3) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
(4) How much loan did Emily borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8437.5 to clear it?
(5) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.
(6) If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.
(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 3 years.
(9) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9512 to clear the loan, then find the time period of the loan.
(10) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.