Question:
Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 4 years.
Correct Answer
$3920
Solution And Explanation
Solution
Given,
Principal (P) = $3500
Rate of Simple Interest (SI) = 3%
Time (t) = 4 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) = $3500 × 3% × 4
= $3500 ×3/100 × 4
= 3500 × 3 × 4/100
= 10500 × 4/100
= 42000/100
= $420
Thus, Simple Interest = $420
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 = $3500 + $420
= $3920
Thus, Amount to be paid = $3920 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 = $3500
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 4 years
Thus, Amount (A)
= $3500 + ($3500 × 3% × 4)
= $3500 + ($3500 ×3/100 × 4)
= $3500 + (3500 × 3 × 4/100)
= $3500 + (10500 × 4/100)
= $3500 + (42000/100)
= $3500 + $420 = $3920
Thus, Amount (A) to be paid = $3920 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 $3500, the simple interest in 1 year
= 3/100 × 3500
= 3 × 3500/100
= 10500/100 = $105
Thus, simple interest for 1 year = $105
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $105 × 4 = $420
Thus, Simple Interest (SI) = $420
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $420
= $3920
Thus, Amount to be paid = $3920 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(2) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.
(3) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(4) Robert had to pay $3379 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.
(6) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 8 years.
(7) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 3% simple interest?
(9) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(10) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.