Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 8 years.
Correct Answer
$8772
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 9%
Time (t) = 8 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) = $5100 × 9% × 8
= $5100 ×9/100 × 8
= 5100 × 9 × 8/100
= 45900 × 8/100
= 367200/100
= $3672
Thus, Simple Interest = $3672
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 = $5100 + $3672
= $8772
Thus, Amount to be paid = $8772 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 = $5100
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5100 + ($5100 × 9% × 8)
= $5100 + ($5100 ×9/100 × 8)
= $5100 + (5100 × 9 × 8/100)
= $5100 + (45900 × 8/100)
= $5100 + (367200/100)
= $5100 + $3672 = $8772
Thus, Amount (A) to be paid = $8772 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 $5100, the simple interest in 1 year
= 9/100 × 5100
= 9 × 5100/100
= 45900/100 = $459
Thus, simple interest for 1 year = $459
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $459 × 8 = $3672
Thus, Simple Interest (SI) = $3672
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $3672
= $8772
Thus, Amount to be paid = $8772 Answer
Similar Questions
(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 8 years.
(2) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.
(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?
(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 7 years.
(5) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?
(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) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan.
(9) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8024 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 4 years.