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) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.
(3) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(4) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(5) How much loan did Lisa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7562.5 to clear it?
(6) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.
(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?
(8) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 3 years.