Question:
Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 5% simple interest.
Correct Answer
$7500
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 5%
Time (t) = 10 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% × 10
= $5000 ×5/100 × 10
= 5000 × 5 × 10/100
= 25000 × 10/100
= 250000/100
= $2500
Thus, Simple Interest = $2500
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 + $2500
= $7500
Thus, Amount to be paid = $7500 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) = 10 years
Thus, Amount (A)
= $5000 + ($5000 × 5% × 10)
= $5000 + ($5000 ×5/100 × 10)
= $5000 + (5000 × 5 × 10/100)
= $5000 + (25000 × 10/100)
= $5000 + (250000/100)
= $5000 + $2500 = $7500
Thus, Amount (A) to be paid = $7500 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 10 years
= Simple interest for 1 year × 10
= $250 × 10 = $2500
Thus, Simple Interest (SI) = $2500
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $2500
= $7500
Thus, Amount to be paid = $7500 Answer
Similar Questions
(1) Joseph had to pay $4033 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 9% simple interest?
(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 4% simple interest?
(4) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?
(5) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 7 years.
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.
(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 4 years.
(9) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.
(10) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8940 to clear the loan, then find the time period of the loan.