Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 8 years.
Correct Answer
$8970
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 7%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 8
= $5750 ×7/100 × 8
= 5750 × 7 × 8/100
= 40250 × 8/100
= 322000/100
= $3220
Thus, Simple Interest = $3220
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 + $3220
= $8970
Thus, Amount to be paid = $8970 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) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5750 + ($5750 × 7% × 8)
= $5750 + ($5750 ×7/100 × 8)
= $5750 + (5750 × 7 × 8/100)
= $5750 + (40250 × 8/100)
= $5750 + (322000/100)
= $5750 + $3220 = $8970
Thus, Amount (A) to be paid = $8970 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5750, the simple interest in 1 year
= 7/100 × 5750
= 7 × 5750/100
= 40250/100 = $402.5
Thus, simple interest for 1 year = $402.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $402.5 × 8 = $3220
Thus, Simple Interest (SI) = $3220
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $3220
= $8970
Thus, Amount to be paid = $8970 Answer
Similar Questions
(1) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?
(2) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.
(3) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 9% simple interest?
(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 3 years.
(5) How much loan did Lisa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6655 to clear it?
(6) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 3 years.
(8) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 3 years.
(9) How much loan did Brian borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9000 to clear it?
(10) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.