Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 4 years.
Correct Answer
$3654
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 4%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $3150 × 4% × 4
= $3150 ×4/100 × 4
= 3150 × 4 × 4/100
= 12600 × 4/100
= 50400/100
= $504
Thus, Simple Interest = $504
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 = $3150 + $504
= $3654
Thus, Amount to be paid = $3654 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 = $3150
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 4 years
Thus, Amount (A)
= $3150 + ($3150 × 4% × 4)
= $3150 + ($3150 ×4/100 × 4)
= $3150 + (3150 × 4 × 4/100)
= $3150 + (12600 × 4/100)
= $3150 + (50400/100)
= $3150 + $504 = $3654
Thus, Amount (A) to be paid = $3654 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $3150, the simple interest in 1 year
= 4/100 × 3150
= 4 × 3150/100
= 12600/100 = $126
Thus, simple interest for 1 year = $126
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $126 × 4 = $504
Thus, Simple Interest (SI) = $504
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $504
= $3654
Thus, Amount to be paid = $3654 Answer
Similar Questions
(1) How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 3 years.
(3) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?
(4) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(6) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9248 to clear the loan, then find the time period of the loan.
(7) How much loan did Brian borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8640 to clear it?
(8) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.
(10) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.