Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 7 years.
Correct Answer
$8567.5
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 7%
Time (t) = 7 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% × 7
= $5750 ×7/100 × 7
= 5750 × 7 × 7/100
= 40250 × 7/100
= 281750/100
= $2817.5
Thus, Simple Interest = $2817.5
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 + $2817.5
= $8567.5
Thus, Amount to be paid = $8567.5 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) = 7 years
Thus, Amount (A)
= $5750 + ($5750 × 7% × 7)
= $5750 + ($5750 ×7/100 × 7)
= $5750 + (5750 × 7 × 7/100)
= $5750 + (40250 × 7/100)
= $5750 + (281750/100)
= $5750 + $2817.5 = $8567.5
Thus, Amount (A) to be paid = $8567.5 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 7 years
= Simple interest for 1 year × 7
= $402.5 × 7 = $2817.5
Thus, Simple Interest (SI) = $2817.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $2817.5
= $8567.5
Thus, Amount to be paid = $8567.5 Answer
Similar Questions
(1) Susan had to pay $4197.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Joshua had to pay $5341 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?
(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 3% simple interest?
(5) How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?
(6) How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?
(7) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?
(8) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(9) What amount does William have to pay after 6 years if he takes a loan of $3500 at 6% simple interest?
(10) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 10% simple interest?