Question:
Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 3 years.
Correct Answer
$4012
Solution And Explanation
Solution
Given,
Principal (P) = $3400
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) = $3400 × 6% × 3
= $3400 ×6/100 × 3
= 3400 × 6 × 3/100
= 20400 × 3/100
= 61200/100
= $612
Thus, Simple Interest = $612
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 = $3400 + $612
= $4012
Thus, Amount to be paid = $4012 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 = $3400
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 3 years
Thus, Amount (A)
= $3400 + ($3400 × 6% × 3)
= $3400 + ($3400 ×6/100 × 3)
= $3400 + (3400 × 6 × 3/100)
= $3400 + (20400 × 3/100)
= $3400 + (61200/100)
= $3400 + $612 = $4012
Thus, Amount (A) to be paid = $4012 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 $3400, the simple interest in 1 year
= 6/100 × 3400
= 6 × 3400/100
= 20400/100 = $204
Thus, simple interest for 1 year = $204
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $204 × 3 = $612
Thus, Simple Interest (SI) = $612
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $612
= $4012
Thus, Amount to be paid = $4012 Answer
Similar Questions
(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 7 years.
(2) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(3) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 4 years.
(5) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
(6) If Nancy paid $4814 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 5% simple interest?
(8) How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?
(9) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.