Question:
Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.
Correct Answer
$8175
Solution And Explanation
Solution
Given,
Principal (P) = $5450
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) = $5450 × 5% × 10
= $5450 ×5/100 × 10
= 5450 × 5 × 10/100
= 27250 × 10/100
= 272500/100
= $2725
Thus, Simple Interest = $2725
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 = $5450 + $2725
= $8175
Thus, Amount to be paid = $8175 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 = $5450
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5450 + ($5450 × 5% × 10)
= $5450 + ($5450 ×5/100 × 10)
= $5450 + (5450 × 5 × 10/100)
= $5450 + (27250 × 10/100)
= $5450 + (272500/100)
= $5450 + $2725 = $8175
Thus, Amount (A) to be paid = $8175 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 $5450, the simple interest in 1 year
= 5/100 × 5450
= 5 × 5450/100
= 27250/100 = $272.5
Thus, simple interest for 1 year = $272.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $272.5 × 10 = $2725
Thus, Simple Interest (SI) = $2725
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $2725
= $8175
Thus, Amount to be paid = $8175 Answer
Similar Questions
(1) 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.
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.
(3) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.
(4) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(5) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.
(7) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(8) If Donald paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.
(10) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?