Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.
Correct Answer
$4216
Solution And Explanation
Solution
Given,
Principal (P) = $3100
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) = $3100 × 9% × 4
= $3100 ×9/100 × 4
= 3100 × 9 × 4/100
= 27900 × 4/100
= 111600/100
= $1116
Thus, Simple Interest = $1116
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 + $1116
= $4216
Thus, Amount to be paid = $4216 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) = 4 years
Thus, Amount (A)
= $3100 + ($3100 × 9% × 4)
= $3100 + ($3100 ×9/100 × 4)
= $3100 + (3100 × 9 × 4/100)
= $3100 + (27900 × 4/100)
= $3100 + (111600/100)
= $3100 + $1116 = $4216
Thus, Amount (A) to be paid = $4216 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 4 years
= Simple interest for 1 year × 4
= $279 × 4 = $1116
Thus, Simple Interest (SI) = $1116
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $1116
= $4216
Thus, Amount to be paid = $4216 Answer
Similar Questions
(1) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(2) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) If Robert paid $3596 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) Sarah had to pay $4312 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?
(6) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(7) How much loan did Brian borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7920 to clear it?
(8) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
(9) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?
(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 8 years.