Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.
Correct Answer
$7762.5
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 5%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 7
= $5750 ×5/100 × 7
= 5750 × 5 × 7/100
= 28750 × 7/100
= 201250/100
= $2012.5
Thus, Simple Interest = $2012.5
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 + $2012.5
= $7762.5
Thus, Amount to be paid = $7762.5 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) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5750 + ($5750 × 5% × 7)
= $5750 + ($5750 ×5/100 × 7)
= $5750 + (5750 × 5 × 7/100)
= $5750 + (28750 × 7/100)
= $5750 + (201250/100)
= $5750 + $2012.5 = $7762.5
Thus, Amount (A) to be paid = $7762.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5750, the simple interest in 1 year
= 5/100 × 5750
= 5 × 5750/100
= 28750/100 = $287.5
Thus, simple interest for 1 year = $287.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $287.5 × 7 = $2012.5
Thus, Simple Interest (SI) = $2012.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $2012.5
= $7762.5
Thus, Amount to be paid = $7762.5 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 8 years.
(4) In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?
(5) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?
(6) In how much time a principal of $3150 will amount to $3528 at a simple interest of 3% per annum?
(7) How much loan did Linda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6420 to clear it?
(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 3 years.
(9) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?
(10) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 3% simple interest.