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) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 7 years.
(2) If Donald paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.
(4) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(5) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 2% simple interest?
(6) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.
(7) Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?
(9) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 5% simple interest.
(10) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.