Question:
Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 3 years.
Correct Answer
$4719
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 7%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $3900 × 7% × 3
= $3900 ×7/100 × 3
= 3900 × 7 × 3/100
= 27300 × 3/100
= 81900/100
= $819
Thus, Simple Interest = $819
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 = $3900 + $819
= $4719
Thus, Amount to be paid = $4719 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 = $3900
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 3 years
Thus, Amount (A)
= $3900 + ($3900 × 7% × 3)
= $3900 + ($3900 ×7/100 × 3)
= $3900 + (3900 × 7 × 3/100)
= $3900 + (27300 × 3/100)
= $3900 + (81900/100)
= $3900 + $819 = $4719
Thus, Amount (A) to be paid = $4719 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3900, the simple interest in 1 year
= 7/100 × 3900
= 7 × 3900/100
= 27300/100 = $273
Thus, simple interest for 1 year = $273
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $273 × 3 = $819
Thus, Simple Interest (SI) = $819
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $819
= $4719
Thus, Amount to be paid = $4719 Answer
Similar Questions
(1) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(2) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 8 years.
(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 8 years.
(4) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.
(5) How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?
(6) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.
(7) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 4 years.
(9) If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) In how much time a principal of $3100 will amount to $3472 at a simple interest of 4% per annum?