Question:
Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.
Correct Answer
$5800
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 2%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 8
= $5000 ×2/100 × 8
= 5000 × 2 × 8/100
= 10000 × 8/100
= 80000/100
= $800
Thus, Simple Interest = $800
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 + $800
= $5800
Thus, Amount to be paid = $5800 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) = 2%
And, Time (t) = 8 years
Thus, Amount (A)
= $5000 + ($5000 × 2% × 8)
= $5000 + ($5000 ×2/100 × 8)
= $5000 + (5000 × 2 × 8/100)
= $5000 + (10000 × 8/100)
= $5000 + (80000/100)
= $5000 + $800 = $5800
Thus, Amount (A) to be paid = $5800 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5000, the simple interest in 1 year
= 2/100 × 5000
= 2 × 5000/100
= 10000/100 = $100
Thus, simple interest for 1 year = $100
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $100 × 8 = $800
Thus, Simple Interest (SI) = $800
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $800
= $5800
Thus, Amount to be paid = $5800 Answer
Similar Questions
(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 8 years.
(2) If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) James had to pay $3270 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12308 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 4 years.
(6) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(7) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 3% simple interest?
(8) How much loan did Brian borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9000 to clear it?
(9) How much loan did Ashley borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7532.5 to clear it?
(10) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.