Question:
Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 8 years.
Correct Answer
$10800
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 8
= $6000 ×10/100 × 8
= 6000 × 10 × 8/100
= 60000 × 8/100
= 480000/100
= $4800
Thus, Simple Interest = $4800
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 + $4800
= $10800
Thus, Amount to be paid = $10800 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $6000 + ($6000 × 10% × 8)
= $6000 + ($6000 ×10/100 × 8)
= $6000 + (6000 × 10 × 8/100)
= $6000 + (60000 × 8/100)
= $6000 + (480000/100)
= $6000 + $4800 = $10800
Thus, Amount (A) to be paid = $10800 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $6000, the simple interest in 1 year
= 10/100 × 6000
= 10 × 6000/100
= 60000/100 = $600
Thus, simple interest for 1 year = $600
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $600 × 8 = $4800
Thus, Simple Interest (SI) = $4800
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $4800
= $10800
Thus, Amount to be paid = $10800 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.
(2) How much loan did Jessica borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6612.5 to clear it?
(3) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 7% simple interest?
(4) Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 4 years.
(6) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 to clear the loan, then find the time period of the loan.
(7) Sarah had to pay $4312 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 7 years.
(9) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 3 years.
(10) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.