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) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 4 years.
(2) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(3) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?
(4) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 4 years.
(6) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?
(8) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?
(9) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.
(10) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.