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) What amount will be due after 2 years if James borrowed a sum of $3000 at a 9% simple interest?
(2) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 6% simple interest?
(3) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
(5) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.
(7) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 6% simple interest?
(8) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(9) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.
(10) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 3% simple interest?