Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 8 years.
Correct Answer
$9890
Solution And Explanation
Solution
Given,
Principal (P) = $5750
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) = $5750 × 9% × 8
= $5750 ×9/100 × 8
= 5750 × 9 × 8/100
= 51750 × 8/100
= 414000/100
= $4140
Thus, Simple Interest = $4140
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 = $5750 + $4140
= $9890
Thus, Amount to be paid = $9890 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 = $5750
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5750 + ($5750 × 9% × 8)
= $5750 + ($5750 ×9/100 × 8)
= $5750 + (5750 × 9 × 8/100)
= $5750 + (51750 × 8/100)
= $5750 + (414000/100)
= $5750 + $4140 = $9890
Thus, Amount (A) to be paid = $9890 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 $5750, the simple interest in 1 year
= 9/100 × 5750
= 9 × 5750/100
= 51750/100 = $517.5
Thus, simple interest for 1 year = $517.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $517.5 × 8 = $4140
Thus, Simple Interest (SI) = $4140
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $4140
= $9890
Thus, Amount to be paid = $9890 Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(2) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 4 years.
(4) In how much time a principal of $3200 will amount to $4000 at a simple interest of 5% per annum?
(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?
(6) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
(7) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(8) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.
(9) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(10) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.