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) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 7 years.
(3) If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 7% simple interest?
(5) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 7 years.
(6) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.
(7) Ashley had to pay $5096 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 7% simple interest?
(9) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 4 years.
(10) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.