Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 3 years.
Correct Answer
$3472
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 4%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 3
= $3100 ×4/100 × 3
= 3100 × 4 × 3/100
= 12400 × 3/100
= 37200/100
= $372
Thus, Simple Interest = $372
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 + $372
= $3472
Thus, Amount to be paid = $3472 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) = 4%
And, Time (t) = 3 years
Thus, Amount (A)
= $3100 + ($3100 × 4% × 3)
= $3100 + ($3100 ×4/100 × 3)
= $3100 + (3100 × 4 × 3/100)
= $3100 + (12400 × 3/100)
= $3100 + (37200/100)
= $3100 + $372 = $3472
Thus, Amount (A) to be paid = $3472 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $3100, the simple interest in 1 year
= 4/100 × 3100
= 4 × 3100/100
= 12400/100 = $124
Thus, simple interest for 1 year = $124
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $124 × 3 = $372
Thus, Simple Interest (SI) = $372
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $372
= $3472
Thus, Amount to be paid = $3472 Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 8 years.
(3) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.
(4) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
(5) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.
(6) If Emily paid $5130 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?
(8) William had to pay $4025 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
(10) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.