Question:
Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.
Correct Answer
$4760
Solution And Explanation
Solution
Given,
Principal (P) = $3500
Rate of Simple Interest (SI) = 9%
Time (t) = 4 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) = $3500 × 9% × 4
= $3500 ×9/100 × 4
= 3500 × 9 × 4/100
= 31500 × 4/100
= 126000/100
= $1260
Thus, Simple Interest = $1260
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 = $3500 + $1260
= $4760
Thus, Amount to be paid = $4760 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 = $3500
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 4 years
Thus, Amount (A)
= $3500 + ($3500 × 9% × 4)
= $3500 + ($3500 ×9/100 × 4)
= $3500 + (3500 × 9 × 4/100)
= $3500 + (31500 × 4/100)
= $3500 + (126000/100)
= $3500 + $1260 = $4760
Thus, Amount (A) to be paid = $4760 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 $3500, the simple interest in 1 year
= 9/100 × 3500
= 9 × 3500/100
= 31500/100 = $315
Thus, simple interest for 1 year = $315
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $315 × 4 = $1260
Thus, Simple Interest (SI) = $1260
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $1260
= $4760
Thus, Amount to be paid = $4760 Answer
Similar Questions
(1) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?
(3) Michael had to pay $3597 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) How much loan did Amanda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8580 to clear it?
(5) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 8 years.
(6) How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?
(7) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(8) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
(9) Patricia had to pay $3339 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.