Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.
Correct Answer
$8050
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 5%
Time (t) = 8 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% × 8
= $5750 ×5/100 × 8
= 5750 × 5 × 8/100
= 28750 × 8/100
= 230000/100
= $2300
Thus, Simple Interest = $2300
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 + $2300
= $8050
Thus, Amount to be paid = $8050 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) = 8 years
Thus, Amount (A)
= $5750 + ($5750 × 5% × 8)
= $5750 + ($5750 ×5/100 × 8)
= $5750 + (5750 × 5 × 8/100)
= $5750 + (28750 × 8/100)
= $5750 + (230000/100)
= $5750 + $2300 = $8050
Thus, Amount (A) to be paid = $8050 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 8 years
= Simple interest for 1 year × 8
= $287.5 × 8 = $2300
Thus, Simple Interest (SI) = $2300
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $2300
= $8050
Thus, Amount to be paid = $8050 Answer
Similar Questions
(1) If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) How much loan did Mary borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6312.5 to clear it?
(3) How much loan did Nancy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7380 to clear it?
(4) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(5) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(6) Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 8 years.
(9) Mary had to pay $3233 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.