Question:
Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 3 years.
Correct Answer
$3270
Solution And Explanation
Solution
Given,
Principal (P) = $3000
Rate of Simple Interest (SI) = 3%
Time (t) = 3 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) = $3000 × 3% × 3
= $3000 ×3/100 × 3
= 3000 × 3 × 3/100
= 9000 × 3/100
= 27000/100
= $270
Thus, Simple Interest = $270
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 + $270
= $3270
Thus, Amount to be paid = $3270 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) = 3%
And, Time (t) = 3 years
Thus, Amount (A)
= $3000 + ($3000 × 3% × 3)
= $3000 + ($3000 ×3/100 × 3)
= $3000 + (3000 × 3 × 3/100)
= $3000 + (9000 × 3/100)
= $3000 + (27000/100)
= $3000 + $270 = $3270
Thus, Amount (A) to be paid = $3270 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 $3000, the simple interest in 1 year
= 3/100 × 3000
= 3 × 3000/100
= 9000/100 = $90
Thus, simple interest for 1 year = $90
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $90 × 3 = $270
Thus, Simple Interest (SI) = $270
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3000 + $270
= $3270
Thus, Amount to be paid = $3270 Answer
Similar Questions
(1) If Robert paid $3348 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 8 years.
(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 3 years.
(4) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.
(5) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?
(7) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.
(8) What amount does William have to pay after 5 years if he takes a loan of $3500 at 8% simple interest?
(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 10% simple interest?
(10) In how much time a principal of $3200 will amount to $3392 at a simple interest of 3% per annum?