Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 7 years.
Correct Answer
$9372.5
Solution And Explanation
Solution
Given,
Principal (P) = $5750
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) = $5750 × 9% × 7
= $5750 ×9/100 × 7
= 5750 × 9 × 7/100
= 51750 × 7/100
= 362250/100
= $3622.5
Thus, Simple Interest = $3622.5
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 = $5750 + $3622.5
= $9372.5
Thus, Amount to be paid = $9372.5 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 = $5750
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 7 years
Thus, Amount (A)
= $5750 + ($5750 × 9% × 7)
= $5750 + ($5750 ×9/100 × 7)
= $5750 + (5750 × 9 × 7/100)
= $5750 + (51750 × 7/100)
= $5750 + (362250/100)
= $5750 + $3622.5 = $9372.5
Thus, Amount (A) to be paid = $9372.5 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 $5750, the simple interest in 1 year
= 9/100 × 5750
= 9 × 5750/100
= 51750/100 = $517.5
Thus, simple interest for 1 year = $517.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $517.5 × 7 = $3622.5
Thus, Simple Interest (SI) = $3622.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $3622.5
= $9372.5
Thus, Amount to be paid = $9372.5 Answer
Similar Questions
(1) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
(2) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.
(3) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 7 years.
(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.
(6) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 5% simple interest?
(7) Sandra had to pay $4850.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 7 years.
(10) Ashley had to pay $5232.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.