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) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 4 years.
(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 7 years.
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 7 years.
(5) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.
(8) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?
(9) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.
(10) How much loan did Sharon borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9687.5 to clear it?