Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 7 years.
Correct Answer
$8268
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 8%
Time (t) = 7 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) = $5300 × 8% × 7
= $5300 ×8/100 × 7
= 5300 × 8 × 7/100
= 42400 × 7/100
= 296800/100
= $2968
Thus, Simple Interest = $2968
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 = $5300 + $2968
= $8268
Thus, Amount to be paid = $8268 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 = $5300
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 7 years
Thus, Amount (A)
= $5300 + ($5300 × 8% × 7)
= $5300 + ($5300 ×8/100 × 7)
= $5300 + (5300 × 8 × 7/100)
= $5300 + (42400 × 7/100)
= $5300 + (296800/100)
= $5300 + $2968 = $8268
Thus, Amount (A) to be paid = $8268 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 $5300, the simple interest in 1 year
= 8/100 × 5300
= 8 × 5300/100
= 42400/100 = $424
Thus, simple interest for 1 year = $424
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $424 × 7 = $2968
Thus, Simple Interest (SI) = $2968
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $2968
= $8268
Thus, Amount to be paid = $8268 Answer
Similar Questions
(1) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 4 years.
(2) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.
(4) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.
(5) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 3 years.
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 3 years.
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 7 years.
(10) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.