Question:
Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 3 years.
Correct Answer
$4142
Solution And Explanation
Solution
Given,
Principal (P) = $3800
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) = $3800 × 3% × 3
= $3800 ×3/100 × 3
= 3800 × 3 × 3/100
= 11400 × 3/100
= 34200/100
= $342
Thus, Simple Interest = $342
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 = $3800 + $342
= $4142
Thus, Amount to be paid = $4142 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 = $3800
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 3 years
Thus, Amount (A)
= $3800 + ($3800 × 3% × 3)
= $3800 + ($3800 ×3/100 × 3)
= $3800 + (3800 × 3 × 3/100)
= $3800 + (11400 × 3/100)
= $3800 + (34200/100)
= $3800 + $342 = $4142
Thus, Amount (A) to be paid = $4142 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 $3800, the simple interest in 1 year
= 3/100 × 3800
= 3 × 3800/100
= 11400/100 = $114
Thus, simple interest for 1 year = $114
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $114 × 3 = $342
Thus, Simple Interest (SI) = $342
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3800 + $342
= $4142
Thus, Amount to be paid = $4142 Answer
Similar Questions
(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 4% simple interest?
(2) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.
(3) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $7888 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.
(6) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(7) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?
(9) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.