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) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?
(2) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.
(3) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.
(4) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?
(5) Donna had to pay $5577.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) How much loan did Melissa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8452.5 to clear it?
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.
(8) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(9) Robert had to pay $3472 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6724 to clear the loan, then find the time period of the loan.