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 Jennifer borrowed a sum of $5250 at 9% simple interest for 8 years.
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 8 years.
(3) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.
(4) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.
(5) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6390 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 4% simple interest for 4 years.
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 3 years.
(8) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.
(9) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.
(10) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.