Question:
What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?
Correct Answer
$3410
Solution And Explanation
Solution
Given,
Principal (P) = $3100
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) = $3100 × 5% × 2
= $3100 ×5/100 × 2
= 3100 × 5 × 2/100
= 15500 × 2/100
= 31000/100
= $310
Thus, Simple Interest = $310
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 = $3100 + $310
= $3410
Thus, Amount to be paid = $3410 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 = $3100
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 2 years
Thus, Amount (A)
= $3100 + ($3100 × 5% × 2)
= $3100 + ($3100 ×5/100 × 2)
= $3100 + (3100 × 5 × 2/100)
= $3100 + (15500 × 2/100)
= $3100 + (31000/100)
= $3100 + $310 = $3410
Thus, Amount (A) to be paid = $3410 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 $3100, the simple interest in 1 year
= 5/100 × 3100
= 5 × 3100/100
= 15500/100 = $155
Thus, simple interest for 1 year = $155
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $155 × 2 = $310
Thus, Simple Interest (SI) = $310
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $310
= $3410
Thus, Amount to be paid = $3410 Answer
Similar Questions
(1) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6812.5 to clear it?
(2) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(3) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?
(4) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.
(5) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?
(6) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 4 years.
(8) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 8% simple interest?
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 8 years.