Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 8 years.
Correct Answer
$6572
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5300 ×3/100 × 8
= 5300 × 3 × 8/100
= 15900 × 8/100
= 127200/100
= $1272
Thus, Simple Interest = $1272
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 + $1272
= $6572
Thus, Amount to be paid = $6572 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5300 + ($5300 × 3% × 8)
= $5300 + ($5300 ×3/100 × 8)
= $5300 + (5300 × 3 × 8/100)
= $5300 + (15900 × 8/100)
= $5300 + (127200/100)
= $5300 + $1272 = $6572
Thus, Amount (A) to be paid = $6572 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5300, the simple interest in 1 year
= 3/100 × 5300
= 3 × 5300/100
= 15900/100 = $159
Thus, simple interest for 1 year = $159
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $159 × 8 = $1272
Thus, Simple Interest (SI) = $1272
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $1272
= $6572
Thus, Amount to be paid = $6572 Answer
Similar Questions
(1) 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.
(2) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 4 years.
(4) If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.
(6) How much loan did Thomas borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6380 to clear it?
(7) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.
(8) If Robert paid $3596 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(10) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7980 to clear it?