Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.
Correct Answer
$3657
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 2%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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) = $3450 × 2% × 3
= $3450 ×2/100 × 3
= 3450 × 2 × 3/100
= 6900 × 3/100
= 20700/100
= $207
Thus, Simple Interest = $207
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 = $3450 + $207
= $3657
Thus, Amount to be paid = $3657 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 = $3450
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 3 years
Thus, Amount (A)
= $3450 + ($3450 × 2% × 3)
= $3450 + ($3450 ×2/100 × 3)
= $3450 + (3450 × 2 × 3/100)
= $3450 + (6900 × 3/100)
= $3450 + (20700/100)
= $3450 + $207 = $3657
Thus, Amount (A) to be paid = $3657 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $3450, the simple interest in 1 year
= 2/100 × 3450
= 2 × 3450/100
= 6900/100 = $69
Thus, simple interest for 1 year = $69
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $69 × 3 = $207
Thus, Simple Interest (SI) = $207
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $207
= $3657
Thus, Amount to be paid = $3657 Answer
Similar Questions
(1) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12670 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 4 years.
(3) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(4) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.
(5) If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?
(7) In how much time a principal of $3100 will amount to $3348 at a simple interest of 4% per annum?
(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.
(9) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 4 years.