Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 7 years.
Correct Answer
$8567.5
Solution And Explanation
Solution
Given,
Principal (P) = $5750
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) = $5750 × 7% × 7
= $5750 ×7/100 × 7
= 5750 × 7 × 7/100
= 40250 × 7/100
= 281750/100
= $2817.5
Thus, Simple Interest = $2817.5
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 + $2817.5
= $8567.5
Thus, Amount to be paid = $8567.5 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) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5750 + ($5750 × 7% × 7)
= $5750 + ($5750 ×7/100 × 7)
= $5750 + (5750 × 7 × 7/100)
= $5750 + (40250 × 7/100)
= $5750 + (281750/100)
= $5750 + $2817.5 = $8567.5
Thus, Amount (A) to be paid = $8567.5 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 $5750, the simple interest in 1 year
= 7/100 × 5750
= 7 × 5750/100
= 40250/100 = $402.5
Thus, simple interest for 1 year = $402.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $402.5 × 7 = $2817.5
Thus, Simple Interest (SI) = $2817.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $2817.5
= $8567.5
Thus, Amount to be paid = $8567.5 Answer
Similar Questions
(1) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 2% simple interest.
(2) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
(3) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.
(4) If Thomas paid $4560 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(6) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?
(7) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
(8) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?
(9) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 5% simple interest?
(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 4 years.