Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 8 years.
Correct Answer
$7590
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 4%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 8
= $5750 ×4/100 × 8
= 5750 × 4 × 8/100
= 23000 × 8/100
= 184000/100
= $1840
Thus, Simple Interest = $1840
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 + $1840
= $7590
Thus, Amount to be paid = $7590 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) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5750 + ($5750 × 4% × 8)
= $5750 + ($5750 ×4/100 × 8)
= $5750 + (5750 × 4 × 8/100)
= $5750 + (23000 × 8/100)
= $5750 + (184000/100)
= $5750 + $1840 = $7590
Thus, Amount (A) to be paid = $7590 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5750, the simple interest in 1 year
= 4/100 × 5750
= 4 × 5750/100
= 23000/100 = $230
Thus, simple interest for 1 year = $230
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $230 × 8 = $1840
Thus, Simple Interest (SI) = $1840
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $1840
= $7590
Thus, Amount to be paid = $7590 Answer
Similar Questions
(1) What amount does John have to pay after 5 years if he takes a loan of $3200 at 9% simple interest?
(2) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 10% simple interest?
(4) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 9% simple interest?
(5) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.
(7) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 4 years.
(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.
(10) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7450 to clear the loan, then find the time period of the loan.