Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 3 years.
Correct Answer
$3937
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 9%
Time (t) = 3 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) = $3100 × 9% × 3
= $3100 ×9/100 × 3
= 3100 × 9 × 3/100
= 27900 × 3/100
= 83700/100
= $837
Thus, Simple Interest = $837
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 = $3100 + $837
= $3937
Thus, Amount to be paid = $3937 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 = $3100
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 3 years
Thus, Amount (A)
= $3100 + ($3100 × 9% × 3)
= $3100 + ($3100 ×9/100 × 3)
= $3100 + (3100 × 9 × 3/100)
= $3100 + (27900 × 3/100)
= $3100 + (83700/100)
= $3100 + $837 = $3937
Thus, Amount (A) to be paid = $3937 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 $3100, the simple interest in 1 year
= 9/100 × 3100
= 9 × 3100/100
= 27900/100 = $279
Thus, simple interest for 1 year = $279
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $279 × 3 = $837
Thus, Simple Interest (SI) = $837
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $837
= $3937
Thus, Amount to be paid = $3937 Answer
Similar Questions
(1) If Michelle paid $5544 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 4 years.
(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.
(4) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.
(5) Christopher had to pay $4240 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) 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?
(7) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?
(8) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 4 years.
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 4 years.
(10) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.