Question:
Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 4 years.
Correct Answer
$4640
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (SI) = 4%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 4
= $4000 ×4/100 × 4
= 4000 × 4 × 4/100
= 16000 × 4/100
= 64000/100
= $640
Thus, Simple Interest = $640
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 + $640
= $4640
Thus, Amount to be paid = $4640 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) = 4%
And, Time (t) = 4 years
Thus, Amount (A)
= $4000 + ($4000 × 4% × 4)
= $4000 + ($4000 ×4/100 × 4)
= $4000 + (4000 × 4 × 4/100)
= $4000 + (16000 × 4/100)
= $4000 + (64000/100)
= $4000 + $640 = $4640
Thus, Amount (A) to be paid = $4640 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $4000, the simple interest in 1 year
= 4/100 × 4000
= 4 × 4000/100
= 16000/100 = $160
Thus, simple interest for 1 year = $160
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $160 × 4 = $640
Thus, Simple Interest (SI) = $640
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $4000 + $640
= $4640
Thus, Amount to be paid = $4640 Answer
Similar Questions
(1) Patricia had to pay $3433.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) What amount does William have to pay after 6 years if he takes a loan of $3500 at 9% simple interest?
(3) 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.
(4) How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?
(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.
(6) How much loan did Karen borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6842.5 to clear it?
(7) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9384 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
(9) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 7 years.