Question:
Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 4 years.
Correct Answer
$4200
Solution And Explanation
Solution
Given,
Principal (P) = $3000
Rate of Simple Interest (SI) = 10%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $3000 × 10% × 4
= $3000 ×10/100 × 4
= 3000 × 10 × 4/100
= 30000 × 4/100
= 120000/100
= $1200
Thus, Simple Interest = $1200
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 = $3000 + $1200
= $4200
Thus, Amount to be paid = $4200 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 = $3000
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 4 years
Thus, Amount (A)
= $3000 + ($3000 × 10% × 4)
= $3000 + ($3000 ×10/100 × 4)
= $3000 + (3000 × 10 × 4/100)
= $3000 + (30000 × 4/100)
= $3000 + (120000/100)
= $3000 + $1200 = $4200
Thus, Amount (A) to be paid = $4200 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3000, the simple interest in 1 year
= 10/100 × 3000
= 10 × 3000/100
= 30000/100 = $300
Thus, simple interest for 1 year = $300
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $300 × 4 = $1200
Thus, Simple Interest (SI) = $1200
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3000 + $1200
= $4200
Thus, Amount to be paid = $4200 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.
(2) James had to pay $3360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?
(4) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(5) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.
(6) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(7) 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?
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 7 years.
(9) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(10) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9685 to clear the loan, then find the time period of the loan.