Question:
Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.
Correct Answer
$7000
Solution And Explanation
Solution
Given,
Principal (P) = $5000
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) = $5000 × 5% × 8
= $5000 ×5/100 × 8
= 5000 × 5 × 8/100
= 25000 × 8/100
= 200000/100
= $2000
Thus, Simple Interest = $2000
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 = $5000 + $2000
= $7000
Thus, Amount to be paid = $7000 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 = $5000
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5000 + ($5000 × 5% × 8)
= $5000 + ($5000 ×5/100 × 8)
= $5000 + (5000 × 5 × 8/100)
= $5000 + (25000 × 8/100)
= $5000 + (200000/100)
= $5000 + $2000 = $7000
Thus, Amount (A) to be paid = $7000 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 $5000, the simple interest in 1 year
= 5/100 × 5000
= 5 × 5000/100
= 25000/100 = $250
Thus, simple interest for 1 year = $250
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $250 × 8 = $2000
Thus, Simple Interest (SI) = $2000
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $2000
= $7000
Thus, Amount to be paid = $7000 Answer
Similar Questions
(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.
(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.
(3) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 4% simple interest?
(4) If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 4 years.
(6) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(7) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 3 years.
(9) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 3 years.