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) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.
(2) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
(3) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.
(4) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(5) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 5% simple interest?
(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.
(7) Donna had to pay $5286.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 7 years.
(9) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.