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) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12670 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 5% simple interest.
(3) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.
(4) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 3% simple interest?
(5) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.
(7) 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.
(8) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?
(9) If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.