Question:
If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$4240
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (SI) = 3%
Time (t) = 2 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 2
= $4000 ×3/100 × 2
= 4000 × 3 × 2/100
= 12000 × 2/100
= 24000/100
= $240
Thus, Simple Interest = $240
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 + $240
= $4240
Thus, Amount to be paid = $4240 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) = 3%
And, Time (t) = 2 years
Thus, Amount (A)
= $4000 + ($4000 × 3% × 2)
= $4000 + ($4000 ×3/100 × 2)
= $4000 + (4000 × 3 × 2/100)
= $4000 + (12000 × 2/100)
= $4000 + (24000/100)
= $4000 + $240 = $4240
Thus, Amount (A) to be paid = $4240 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $4000, the simple interest in 1 year
= 3/100 × 4000
= 3 × 4000/100
= 12000/100 = $120
Thus, simple interest for 1 year = $120
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $120 × 2 = $240
Thus, Simple Interest (SI) = $240
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $4000 + $240
= $4240
Thus, Amount to be paid = $4240 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.
(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?
(3) If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 7 years.
(5) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 2% simple interest.
(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 7 years.
(8) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 8 years.
(9) Kenneth had to pay $5600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.