Question:
Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 4 years.
Correct Answer
$4200
Solution And Explanation
Solution
Given,
Principal (P) = $3500
Rate of Simple Interest (SI) = 5%
Time (t) = 4 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) = $3500 × 5% × 4
= $3500 ×5/100 × 4
= 3500 × 5 × 4/100
= 17500 × 4/100
= 70000/100
= $700
Thus, Simple Interest = $700
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 = $3500 + $700
= $4200
Thus, Amount to be paid = $4200 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 = $3500
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 4 years
Thus, Amount (A)
= $3500 + ($3500 × 5% × 4)
= $3500 + ($3500 ×5/100 × 4)
= $3500 + (3500 × 5 × 4/100)
= $3500 + (17500 × 4/100)
= $3500 + (70000/100)
= $3500 + $700 = $4200
Thus, Amount (A) to be paid = $4200 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 $3500, the simple interest in 1 year
= 5/100 × 3500
= 5 × 3500/100
= 17500/100 = $175
Thus, simple interest for 1 year = $175
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $175 × 4 = $700
Thus, Simple Interest (SI) = $700
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $700
= $4200
Thus, Amount to be paid = $4200 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.
(2) In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum?
(3) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(4) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?
(5) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 8 years.
(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 7 years.
(7) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(8) Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 7 years.
(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 3 years.