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) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 4 years.
(3) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 8 years.
(5) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8312.5 to clear it?
(6) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?
(7) In how much time a principal of $3100 will amount to $3596 at a simple interest of 4% per annum?
(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 7 years.
(9) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 9% simple interest?
(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.