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) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.
(3) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(4) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 3 years.
(6) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
(7) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(8) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9184 to clear the loan, then find the time period of the loan.
(9) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3150 will amount to $3339 at a simple interest of 2% per annum?