Question:
Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.
Correct Answer
$5016.5
Solution And Explanation
Solution
Given,
Principal (P) = $3950
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) = $3950 × 9% × 3
= $3950 ×9/100 × 3
= 3950 × 9 × 3/100
= 35550 × 3/100
= 106650/100
= $1066.5
Thus, Simple Interest = $1066.5
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 = $3950 + $1066.5
= $5016.5
Thus, Amount to be paid = $5016.5 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 = $3950
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 3 years
Thus, Amount (A)
= $3950 + ($3950 × 9% × 3)
= $3950 + ($3950 ×9/100 × 3)
= $3950 + (3950 × 9 × 3/100)
= $3950 + (35550 × 3/100)
= $3950 + (106650/100)
= $3950 + $1066.5 = $5016.5
Thus, Amount (A) to be paid = $5016.5 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 $3950, the simple interest in 1 year
= 9/100 × 3950
= 9 × 3950/100
= 35550/100 = $355.5
Thus, simple interest for 1 year = $355.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $355.5 × 3 = $1066.5
Thus, Simple Interest (SI) = $1066.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3950 + $1066.5
= $5016.5
Thus, Amount to be paid = $5016.5 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(2) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 8 years.
(3) William had to pay $4025 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.
(5) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10679 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(7) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(8) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(9) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(10) How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?