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 after 9 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(2) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 7 years.
(4) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.
(5) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 3% simple interest?
(6) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8688 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.
(8) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.
(9) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 4 years.
(10) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 9% simple interest?