Question:
Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
Correct Answer
$7150
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 3%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 10
= $5500 ×3/100 × 10
= 5500 × 3 × 10/100
= 16500 × 10/100
= 165000/100
= $1650
Thus, Simple Interest = $1650
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 + $1650
= $7150
Thus, Amount to be paid = $7150 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) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5500 + ($5500 × 3% × 10)
= $5500 + ($5500 ×3/100 × 10)
= $5500 + (5500 × 3 × 10/100)
= $5500 + (16500 × 10/100)
= $5500 + (165000/100)
= $5500 + $1650 = $7150
Thus, Amount (A) to be paid = $7150 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5500, the simple interest in 1 year
= 3/100 × 5500
= 3 × 5500/100
= 16500/100 = $165
Thus, simple interest for 1 year = $165
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $165 × 10 = $1650
Thus, Simple Interest (SI) = $1650
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $1650
= $7150
Thus, Amount to be paid = $7150 Answer
Similar Questions
(1) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 3 years.
(2) If John paid $3456 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 4 years.
(5) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 9% simple interest?
(6) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?
(7) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.
(9) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(10) If Robert paid $3348 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.