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) In how much time a principal of $3150 will amount to $3276 at a simple interest of 2% per annum?
(2) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?
(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 4 years.
(4) William had to pay $3710 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?
(6) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
(7) How much loan did Susan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6215 to clear it?
(8) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.
(9) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?
(10) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.