Question:
Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
Correct Answer
$11000
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 10%
Time (t) = 10 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) = $5500 × 10% × 10
= $5500 ×10/100 × 10
= 5500 × 10 × 10/100
= 55000 × 10/100
= 550000/100
= $5500
Thus, Simple Interest = $5500
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 = $5500 + $5500
= $11000
Thus, Amount to be paid = $11000 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 = $5500
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 10 years
Thus, Amount (A)
= $5500 + ($5500 × 10% × 10)
= $5500 + ($5500 ×10/100 × 10)
= $5500 + (5500 × 10 × 10/100)
= $5500 + (55000 × 10/100)
= $5500 + (550000/100)
= $5500 + $5500 = $11000
Thus, Amount (A) to be paid = $11000 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 $5500, the simple interest in 1 year
= 10/100 × 5500
= 10 × 5500/100
= 55000/100 = $550
Thus, simple interest for 1 year = $550
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $550 × 10 = $5500
Thus, Simple Interest (SI) = $5500
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $5500
= $11000
Thus, Amount to be paid = $11000 Answer
Similar Questions
(1) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 8% simple interest?
(2) If Joshua paid $5488 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11946 to clear the loan, then find the time period of the loan.
(4) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.
(5) If Christopher paid $4640 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 4 years.
(7) If Donald paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?
(9) Jessica had to pay $3975 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Nancy had to pay $4523.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.