Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.
Correct Answer
$4284
Solution And Explanation
Solution
Given,
Principal (P) = $3150
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) = $3150 × 9% × 4
= $3150 ×9/100 × 4
= 3150 × 9 × 4/100
= 28350 × 4/100
= 113400/100
= $1134
Thus, Simple Interest = $1134
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 = $3150 + $1134
= $4284
Thus, Amount to be paid = $4284 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 = $3150
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 4 years
Thus, Amount (A)
= $3150 + ($3150 × 9% × 4)
= $3150 + ($3150 ×9/100 × 4)
= $3150 + (3150 × 9 × 4/100)
= $3150 + (28350 × 4/100)
= $3150 + (113400/100)
= $3150 + $1134 = $4284
Thus, Amount (A) to be paid = $4284 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 $3150, the simple interest in 1 year
= 9/100 × 3150
= 9 × 3150/100
= 28350/100 = $283.5
Thus, simple interest for 1 year = $283.5
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $283.5 × 4 = $1134
Thus, Simple Interest (SI) = $1134
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $1134
= $4284
Thus, Amount to be paid = $4284 Answer
Similar Questions
(1) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 4 years.
(2) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?
(3) 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.
(4) How much loan did Joshua borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8280 to clear it?
(5) What amount does John have to pay after 6 years if he takes a loan of $3200 at 6% simple interest?
(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 3 years.
(7) Donald had to pay $4770 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 3 years.
(9) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(10) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?