Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.
Correct Answer
$9775
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 10%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 7
= $5750 ×10/100 × 7
= 5750 × 10 × 7/100
= 57500 × 7/100
= 402500/100
= $4025
Thus, Simple Interest = $4025
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 + $4025
= $9775
Thus, Amount to be paid = $9775 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) = 10%
And, Time (t) = 7 years
Thus, Amount (A)
= $5750 + ($5750 × 10% × 7)
= $5750 + ($5750 ×10/100 × 7)
= $5750 + (5750 × 10 × 7/100)
= $5750 + (57500 × 7/100)
= $5750 + (402500/100)
= $5750 + $4025 = $9775
Thus, Amount (A) to be paid = $9775 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5750, the simple interest in 1 year
= 10/100 × 5750
= 10 × 5750/100
= 57500/100 = $575
Thus, simple interest for 1 year = $575
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $575 × 7 = $4025
Thus, Simple Interest (SI) = $4025
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $4025
= $9775
Thus, Amount to be paid = $9775 Answer
Similar Questions
(1) If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 8 years.
(4) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.
(6) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
(7) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(8) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.
(10) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.