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) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 3 years.
(2) Steven had to pay $5014 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 10% simple interest?
(4) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 3 years.
(6) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 8% simple interest?
(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.
(8) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 5% simple interest.
(9) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 8 years.
(10) If Michelle paid $5544 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.