Question:
Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 3 years.
Correct Answer
$4826
Solution And Explanation
Solution
Given,
Principal (P) = $3800
Rate of Simple Interest (SI) = 9%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 3
= $3800 ×9/100 × 3
= 3800 × 9 × 3/100
= 34200 × 3/100
= 102600/100
= $1026
Thus, Simple Interest = $1026
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 + $1026
= $4826
Thus, Amount to be paid = $4826 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) = 9%
And, Time (t) = 3 years
Thus, Amount (A)
= $3800 + ($3800 × 9% × 3)
= $3800 + ($3800 ×9/100 × 3)
= $3800 + (3800 × 9 × 3/100)
= $3800 + (34200 × 3/100)
= $3800 + (102600/100)
= $3800 + $1026 = $4826
Thus, Amount (A) to be paid = $4826 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $3800, the simple interest in 1 year
= 9/100 × 3800
= 9 × 3800/100
= 34200/100 = $342
Thus, simple interest for 1 year = $342
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $342 × 3 = $1026
Thus, Simple Interest (SI) = $1026
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3800 + $1026
= $4826
Thus, Amount to be paid = $4826 Answer
Similar Questions
(1) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(2) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.
(3) If Kimberly paid $5580 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) What amount will be due after 2 years if James borrowed a sum of $3000 at a 4% simple interest?
(5) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 6% simple interest?
(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(7) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?
(8) In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?
(9) What amount does John have to pay after 5 years if he takes a loan of $3200 at 10% simple interest?
(10) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.