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 Susan borrowed a sum of $3650 at 5% simple interest for 3 years.
(2) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7240 to clear the loan, then find the time period of the loan.
(3) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9536 to clear the loan, then find the time period of the loan.
(4) Emily had to pay $5320 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.
(7) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 4 years.
(9) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
(10) 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.