Question:
Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
Correct Answer
$7493
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 3%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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) = $5900 × 3% × 9
= $5900 ×3/100 × 9
= 5900 × 3 × 9/100
= 17700 × 9/100
= 159300/100
= $1593
Thus, Simple Interest = $1593
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 = $5900 + $1593
= $7493
Thus, Amount to be paid = $7493 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 = $5900
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 9 years
Thus, Amount (A)
= $5900 + ($5900 × 3% × 9)
= $5900 + ($5900 ×3/100 × 9)
= $5900 + (5900 × 3 × 9/100)
= $5900 + (17700 × 9/100)
= $5900 + (159300/100)
= $5900 + $1593 = $7493
Thus, Amount (A) to be paid = $7493 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5900, the simple interest in 1 year
= 3/100 × 5900
= 3 × 5900/100
= 17700/100 = $177
Thus, simple interest for 1 year = $177
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $177 × 9 = $1593
Thus, Simple Interest (SI) = $1593
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $1593
= $7493
Thus, Amount to be paid = $7493 Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.
(2) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(3) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?
(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 7 years.
(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
(6) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 7 years.
(8) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(9) How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?
(10) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.