Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 3 years.
Correct Answer
$3528
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 4%
Time (t) = 3 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) = $3150 × 4% × 3
= $3150 ×4/100 × 3
= 3150 × 4 × 3/100
= 12600 × 3/100
= 37800/100
= $378
Thus, Simple Interest = $378
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 = $3150 + $378
= $3528
Thus, Amount to be paid = $3528 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 = $3150
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 3 years
Thus, Amount (A)
= $3150 + ($3150 × 4% × 3)
= $3150 + ($3150 ×4/100 × 3)
= $3150 + (3150 × 4 × 3/100)
= $3150 + (12600 × 3/100)
= $3150 + (37800/100)
= $3150 + $378 = $3528
Thus, Amount (A) to be paid = $3528 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 $3150, the simple interest in 1 year
= 4/100 × 3150
= 4 × 3150/100
= 12600/100 = $126
Thus, simple interest for 1 year = $126
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $126 × 3 = $378
Thus, Simple Interest (SI) = $378
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $378
= $3528
Thus, Amount to be paid = $3528 Answer
Similar Questions
(1) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) If Joseph paid $4292 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?
(5) If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 8 years.
(7) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(8) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(9) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 8 years.