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 10% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 3 years.
(3) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 4 years.
(5) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.
(7) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?
(8) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 9% simple interest?