Question:
If Christopher borrowed $4000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$4160
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (SI) = 2%
Time (t) = 2 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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) = $4000 × 2% × 2
= $4000 ×2/100 × 2
= 4000 × 2 × 2/100
= 8000 × 2/100
= 16000/100
= $160
Thus, Simple Interest = $160
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 = $4000 + $160
= $4160
Thus, Amount to be paid = $4160 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 = $4000
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 2 years
Thus, Amount (A)
= $4000 + ($4000 × 2% × 2)
= $4000 + ($4000 ×2/100 × 2)
= $4000 + (4000 × 2 × 2/100)
= $4000 + (8000 × 2/100)
= $4000 + (16000/100)
= $4000 + $160 = $4160
Thus, Amount (A) to be paid = $4160 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest in 1 year = $2
∴ For $1, the simple interest in 1 year = 2/100
∴ For $4000, the simple interest in 1 year
= 2/100 × 4000
= 2 × 4000/100
= 8000/100 = $80
Thus, simple interest in 1 year = $80
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $80 × 2 = $160
Thus, Simple Interest (SI) = $160
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $4000 + $160
= $4160
Thus, Amount to be paid = $4160 Answer
Similar Questions
(1) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.
(3) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 8% simple interest?
(4) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 3 years.
(5) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 7 years.
(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 8 years.
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 3 years.
(9) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(10) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.