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) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 2% simple interest.
(2) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(3) How much loan did Deborah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8567.5 to clear it?
(4) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.
(5) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12308 to clear the loan, then find the time period of the loan.
(6) What amount does David have to pay after 5 years if he takes a loan of $3400 at 4% simple interest?
(7) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.
(8) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?
(9) How much loan did Patricia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6180 to clear it?
(10) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 8% simple interest?