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) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 8 years.
(2) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.
(3) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?
(4) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.
(5) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?
(6) If Michelle paid $5742 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.
(8) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.
(9) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.
(10) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.