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) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 7 years.
(2) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.
(3) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?
(4) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(5) How much loan did Sandra borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7740 to clear it?
(6) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?
(7) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.
(9) How much loan did Ashley borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8187.5 to clear it?
(10) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?