Question:
Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 8 years.
Correct Answer
$8528
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 8%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $5200 × 8% × 8
= $5200 ×8/100 × 8
= 5200 × 8 × 8/100
= 41600 × 8/100
= 332800/100
= $3328
Thus, Simple Interest = $3328
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 = $5200 + $3328
= $8528
Thus, Amount to be paid = $8528 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 = $5200
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5200 + ($5200 × 8% × 8)
= $5200 + ($5200 ×8/100 × 8)
= $5200 + (5200 × 8 × 8/100)
= $5200 + (41600 × 8/100)
= $5200 + (332800/100)
= $5200 + $3328 = $8528
Thus, Amount (A) to be paid = $8528 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5200, the simple interest in 1 year
= 8/100 × 5200
= 8 × 5200/100
= 41600/100 = $416
Thus, simple interest for 1 year = $416
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $416 × 8 = $3328
Thus, Simple Interest (SI) = $3328
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $3328
= $8528
Thus, Amount to be paid = $8528 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 3 years.
(3) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(5) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.
(6) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(7) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 8 years.
(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 8 years.