Question:
Calculate the amount due if Thomas borrowed a sum of $3800 at 5% simple interest for 3 years.
Correct Answer
$4370
Solution And Explanation
Solution
Given,
Principal (P) = $3800
Rate of Simple Interest (SI) = 5%
Time (t) = 3 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) = $3800 × 5% × 3
= $3800 ×5/100 × 3
= 3800 × 5 × 3/100
= 19000 × 3/100
= 57000/100
= $570
Thus, Simple Interest = $570
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 + $570
= $4370
Thus, Amount to be paid = $4370 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) = 5%
And, Time (t) = 3 years
Thus, Amount (A)
= $3800 + ($3800 × 5% × 3)
= $3800 + ($3800 ×5/100 × 3)
= $3800 + (3800 × 5 × 3/100)
= $3800 + (19000 × 3/100)
= $3800 + (57000/100)
= $3800 + $570 = $4370
Thus, Amount (A) to be paid = $4370 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 $3800, the simple interest in 1 year
= 5/100 × 3800
= 5 × 3800/100
= 19000/100 = $190
Thus, simple interest for 1 year = $190
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $190 × 3 = $570
Thus, Simple Interest (SI) = $570
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3800 + $570
= $4370
Thus, Amount to be paid = $4370 Answer
Similar Questions
(1) How much loan did Daniel borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6710 to clear it?
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 7 years.
(3) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(4) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 3 years.
(6) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 7% simple interest?
(7) Patricia had to pay $3339 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.
(9) If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.