Question:
What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 5% simple interest?
Correct Answer
$3850
Solution And Explanation
Solution
Given,
Principal (P) = $3500
Rate of Simple Interest (SI) = 5%
Time (t) = 2 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) = $3500 × 5% × 2
= $3500 ×5/100 × 2
= 3500 × 5 × 2/100
= 17500 × 2/100
= 35000/100
= $350
Thus, Simple Interest = $350
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 + $350
= $3850
Thus, Amount to be paid = $3850 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) = 5%
And, Time (t) = 2 years
Thus, Amount (A)
= $3500 + ($3500 × 5% × 2)
= $3500 + ($3500 ×5/100 × 2)
= $3500 + (3500 × 5 × 2/100)
= $3500 + (17500 × 2/100)
= $3500 + (35000/100)
= $3500 + $350 = $3850
Thus, Amount (A) to be paid = $3850 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 $3500, the simple interest in 1 year
= 5/100 × 3500
= 5 × 3500/100
= 17500/100 = $175
Thus, simple interest for 1 year = $175
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $175 × 2 = $350
Thus, Simple Interest (SI) = $350
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $350
= $3850
Thus, Amount to be paid = $3850 Answer
Similar Questions
(1) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 3 years.
(2) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.
(4) If Betty paid $4930 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 6% simple interest?
(7) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 4% simple interest?
(8) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(9) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(10) If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.