Question:
Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.
Correct Answer
$3810
Solution And Explanation
Solution
Given,
Principal (P) = $3000
Rate of Simple Interest (SI) = 9%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 3
= $3000 ×9/100 × 3
= 3000 × 9 × 3/100
= 27000 × 3/100
= 81000/100
= $810
Thus, Simple Interest = $810
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 + $810
= $3810
Thus, Amount to be paid = $3810 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) = 9%
And, Time (t) = 3 years
Thus, Amount (A)
= $3000 + ($3000 × 9% × 3)
= $3000 + ($3000 ×9/100 × 3)
= $3000 + (3000 × 9 × 3/100)
= $3000 + (27000 × 3/100)
= $3000 + (81000/100)
= $3000 + $810 = $3810
Thus, Amount (A) to be paid = $3810 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $3000, the simple interest in 1 year
= 9/100 × 3000
= 9 × 3000/100
= 27000/100 = $270
Thus, simple interest for 1 year = $270
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $270 × 3 = $810
Thus, Simple Interest (SI) = $810
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3000 + $810
= $3810
Thus, Amount to be paid = $3810 Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.
(3) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.
(5) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(6) Michael had to pay $3795 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 8 years.
(8) Paul had to pay $5123 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?
(10) In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?