Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 7 years.
Correct Answer
$9535.5
Solution And Explanation
Solution
Given,
Principal (P) = $5850
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) = $5850 × 9% × 7
= $5850 ×9/100 × 7
= 5850 × 9 × 7/100
= 52650 × 7/100
= 368550/100
= $3685.5
Thus, Simple Interest = $3685.5
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 = $5850 + $3685.5
= $9535.5
Thus, Amount to be paid = $9535.5 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 = $5850
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 7 years
Thus, Amount (A)
= $5850 + ($5850 × 9% × 7)
= $5850 + ($5850 ×9/100 × 7)
= $5850 + (5850 × 9 × 7/100)
= $5850 + (52650 × 7/100)
= $5850 + (368550/100)
= $5850 + $3685.5 = $9535.5
Thus, Amount (A) to be paid = $9535.5 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 $5850, the simple interest in 1 year
= 9/100 × 5850
= 9 × 5850/100
= 52650/100 = $526.5
Thus, simple interest for 1 year = $526.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $526.5 × 7 = $3685.5
Thus, Simple Interest (SI) = $3685.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $3685.5
= $9535.5
Thus, Amount to be paid = $9535.5 Answer
Similar Questions
(1) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10679 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 3 years.
(3) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?
(5) How much loan did Lisa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7260 to clear it?
(6) 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.
(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
(8) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 3 years.
(9) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.
(10) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.