Question:
Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 3 years.
Correct Answer
$3815
Solution And Explanation
Solution
Given,
Principal (P) = $3500
Rate of Simple Interest (SI) = 3%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 3
= $3500 ×3/100 × 3
= 3500 × 3 × 3/100
= 10500 × 3/100
= 31500/100
= $315
Thus, Simple Interest = $315
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 + $315
= $3815
Thus, Amount to be paid = $3815 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) = 3%
And, Time (t) = 3 years
Thus, Amount (A)
= $3500 + ($3500 × 3% × 3)
= $3500 + ($3500 ×3/100 × 3)
= $3500 + (3500 × 3 × 3/100)
= $3500 + (10500 × 3/100)
= $3500 + (31500/100)
= $3500 + $315 = $3815
Thus, Amount (A) to be paid = $3815 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3500, the simple interest in 1 year
= 3/100 × 3500
= 3 × 3500/100
= 10500/100 = $105
Thus, simple interest for 1 year = $105
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $105 × 3 = $315
Thus, Simple Interest (SI) = $315
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $315
= $3815
Thus, Amount to be paid = $3815 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 $6528 to clear the loan, then find the time period of the loan.
(2) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(3) Thomas had to pay $4028 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) If John paid $3456 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(7) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $8400 to clear the loan, then find the time period of the loan.
(8) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.
(9) If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?