Question:
Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
Correct Answer
$6350
Solution And Explanation
Solution
Given,
Principal (P) = $5000
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) = $5000 × 3% × 9
= $5000 ×3/100 × 9
= 5000 × 3 × 9/100
= 15000 × 9/100
= 135000/100
= $1350
Thus, Simple Interest = $1350
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 = $5000 + $1350
= $6350
Thus, Amount to be paid = $6350 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 = $5000
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 9 years
Thus, Amount (A)
= $5000 + ($5000 × 3% × 9)
= $5000 + ($5000 ×3/100 × 9)
= $5000 + (5000 × 3 × 9/100)
= $5000 + (15000 × 9/100)
= $5000 + (135000/100)
= $5000 + $1350 = $6350
Thus, Amount (A) to be paid = $6350 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 $5000, the simple interest in 1 year
= 3/100 × 5000
= 3 × 5000/100
= 15000/100 = $150
Thus, simple interest for 1 year = $150
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $150 × 9 = $1350
Thus, Simple Interest (SI) = $1350
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $1350
= $6350
Thus, Amount to be paid = $6350 Answer
Similar Questions
(1) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(2) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?
(3) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(5) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.
(7) If Christopher paid $4640 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 8 years.
(10) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8344 to clear the loan, then find the time period of the loan.