Question:
Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.
Correct Answer
$8400
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 5%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $6000 × 5% × 8
= $6000 ×5/100 × 8
= 6000 × 5 × 8/100
= 30000 × 8/100
= 240000/100
= $2400
Thus, Simple Interest = $2400
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 = $6000 + $2400
= $8400
Thus, Amount to be paid = $8400 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 = $6000
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $6000 + ($6000 × 5% × 8)
= $6000 + ($6000 ×5/100 × 8)
= $6000 + (6000 × 5 × 8/100)
= $6000 + (30000 × 8/100)
= $6000 + (240000/100)
= $6000 + $2400 = $8400
Thus, Amount (A) to be paid = $8400 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $6000, the simple interest in 1 year
= 5/100 × 6000
= 5 × 6000/100
= 30000/100 = $300
Thus, simple interest for 1 year = $300
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $300 × 8 = $2400
Thus, Simple Interest (SI) = $2400
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $2400
= $8400
Thus, Amount to be paid = $8400 Answer
Similar Questions
(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 8 years.
(2) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 7% simple interest?
(3) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(5) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.
(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(7) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 7 years.
(9) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.
(10) How much loan did Mary borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5807.5 to clear it?