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) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.
(2) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.
(3) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(4) How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?
(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.
(6) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 3 years.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 8 years.
(8) Paul had to pay $5123 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 5% simple interest?
(10) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.