Question:
Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 4 years.
Correct Answer
$4080
Solution And Explanation
Solution
Given,
Principal (P) = $3400
Rate of Simple Interest (SI) = 5%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 4
= $3400 ×5/100 × 4
= 3400 × 5 × 4/100
= 17000 × 4/100
= 68000/100
= $680
Thus, Simple Interest = $680
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 + $680
= $4080
Thus, Amount to be paid = $4080 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) = 5%
And, Time (t) = 4 years
Thus, Amount (A)
= $3400 + ($3400 × 5% × 4)
= $3400 + ($3400 ×5/100 × 4)
= $3400 + (3400 × 5 × 4/100)
= $3400 + (17000 × 4/100)
= $3400 + (68000/100)
= $3400 + $680 = $4080
Thus, Amount (A) to be paid = $4080 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3400, the simple interest in 1 year
= 5/100 × 3400
= 5 × 3400/100
= 17000/100 = $170
Thus, simple interest for 1 year = $170
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $170 × 4 = $680
Thus, Simple Interest (SI) = $680
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3400 + $680
= $4080
Thus, Amount to be paid = $4080 Answer
Similar Questions
(1) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 4 years.
(2) If Steven paid $5336 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 7 years.
(4) Barbara had to pay $3763 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12800 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 7 years.
(7) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6664 to clear the loan, then find the time period of the loan.
(8) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) If Sandra paid $5162 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) If Donald paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.