Question:
What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?
Correct Answer
$5800
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (SI) = 9%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 5
= $4000 ×9/100 × 5
= 4000 × 9 × 5/100
= 36000 × 5/100
= 180000/100
= $1800
Thus, Simple Interest = $1800
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 + $1800
= $5800
Thus, Amount to be paid = $5800 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) = 9%
And, Time (t) = 5 years
Thus, Amount (A)
= $4000 + ($4000 × 9% × 5)
= $4000 + ($4000 ×9/100 × 5)
= $4000 + (4000 × 9 × 5/100)
= $4000 + (36000 × 5/100)
= $4000 + (180000/100)
= $4000 + $1800 = $5800
Thus, Amount (A) to be paid = $5800 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $4000, the simple interest in 1 year
= 9/100 × 4000
= 9 × 4000/100
= 36000/100 = $360
Thus, simple interest for 1 year = $360
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $360 × 5 = $1800
Thus, Simple Interest (SI) = $1800
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $4000 + $1800
= $5800
Thus, Amount to be paid = $5800 Answer
Similar Questions
(1) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?
(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(3) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.
(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 7 years.
(6) John had to pay $3392 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) What amount will be due after 2 years if James borrowed a sum of $3000 at a 8% simple interest?
(8) If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 3 years.
(10) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.