Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 3 years.
Correct Answer
$3717
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 6%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 3
= $3150 ×6/100 × 3
= 3150 × 6 × 3/100
= 18900 × 3/100
= 56700/100
= $567
Thus, Simple Interest = $567
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 + $567
= $3717
Thus, Amount to be paid = $3717 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) = 6%
And, Time (t) = 3 years
Thus, Amount (A)
= $3150 + ($3150 × 6% × 3)
= $3150 + ($3150 ×6/100 × 3)
= $3150 + (3150 × 6 × 3/100)
= $3150 + (18900 × 3/100)
= $3150 + (56700/100)
= $3150 + $567 = $3717
Thus, Amount (A) to be paid = $3717 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $3150, the simple interest in 1 year
= 6/100 × 3150
= 6 × 3150/100
= 18900/100 = $189
Thus, simple interest for 1 year = $189
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $189 × 3 = $567
Thus, Simple Interest (SI) = $567
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $567
= $3717
Thus, Amount to be paid = $3717 Answer
Similar Questions
(1) If Nancy paid $4482 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?
(3) If John paid $3584 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) If Jessica paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 4 years.
(6) How much loan did Mary borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6312.5 to clear it?
(7) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?
(8) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 8% simple interest?
(10) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $6936 to clear the loan, then find the time period of the loan.