Question:
Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 3 years.
Correct Answer
$3706
Solution And Explanation
Solution
Given,
Principal (P) = $3400
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) = $3400 × 3% × 3
= $3400 ×3/100 × 3
= 3400 × 3 × 3/100
= 10200 × 3/100
= 30600/100
= $306
Thus, Simple Interest = $306
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 + $306
= $3706
Thus, Amount to be paid = $3706 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) = 3%
And, Time (t) = 3 years
Thus, Amount (A)
= $3400 + ($3400 × 3% × 3)
= $3400 + ($3400 ×3/100 × 3)
= $3400 + (3400 × 3 × 3/100)
= $3400 + (10200 × 3/100)
= $3400 + (30600/100)
= $3400 + $306 = $3706
Thus, Amount (A) to be paid = $3706 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 $3400, the simple interest in 1 year
= 3/100 × 3400
= 3 × 3400/100
= 10200/100 = $102
Thus, simple interest for 1 year = $102
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $102 × 3 = $306
Thus, Simple Interest (SI) = $306
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $306
= $3706
Thus, Amount to be paid = $3706 Answer
Similar Questions
(1) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(3) How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?
(4) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.
(5) If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 4 years.
(8) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 4 years.
(10) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.