Question:
Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
Correct Answer
$10900
Solution And Explanation
Solution
Given,
Principal (P) = $5450
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) = $5450 × 10% × 10
= $5450 ×10/100 × 10
= 5450 × 10 × 10/100
= 54500 × 10/100
= 545000/100
= $5450
Thus, Simple Interest = $5450
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 + $5450
= $10900
Thus, Amount to be paid = $10900 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) = 10%
And, Time (t) = 10 years
Thus, Amount (A)
= $5450 + ($5450 × 10% × 10)
= $5450 + ($5450 ×10/100 × 10)
= $5450 + (5450 × 10 × 10/100)
= $5450 + (54500 × 10/100)
= $5450 + (545000/100)
= $5450 + $5450 = $10900
Thus, Amount (A) to be paid = $10900 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 $5450, the simple interest in 1 year
= 10/100 × 5450
= 10 × 5450/100
= 54500/100 = $545
Thus, simple interest for 1 year = $545
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $545 × 10 = $5450
Thus, Simple Interest (SI) = $5450
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $5450
= $10900
Thus, Amount to be paid = $10900 Answer
Similar Questions
(1) If Kenneth paid $5600 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?
(3) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 9% simple interest?
(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 3 years.
(5) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
(6) How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 3 years.
(8) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.
(9) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 4 years.