Question:
Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.
Correct Answer
$6921.5
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 3%
Time (t) = 9 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) = $5450 × 3% × 9
= $5450 ×3/100 × 9
= 5450 × 3 × 9/100
= 16350 × 9/100
= 147150/100
= $1471.5
Thus, Simple Interest = $1471.5
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 + $1471.5
= $6921.5
Thus, Amount to be paid = $6921.5 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) = 3%
And, Time (t) = 9 years
Thus, Amount (A)
= $5450 + ($5450 × 3% × 9)
= $5450 + ($5450 ×3/100 × 9)
= $5450 + (5450 × 3 × 9/100)
= $5450 + (16350 × 9/100)
= $5450 + (147150/100)
= $5450 + $1471.5 = $6921.5
Thus, Amount (A) to be paid = $6921.5 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 $5450, the simple interest in 1 year
= 3/100 × 5450
= 3 × 5450/100
= 16350/100 = $163.5
Thus, simple interest for 1 year = $163.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $163.5 × 9 = $1471.5
Thus, Simple Interest (SI) = $1471.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $1471.5
= $6921.5
Thus, Amount to be paid = $6921.5 Answer
Similar Questions
(1) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 4 years.
(2) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.
(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 3 years.
(4) How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?
(5) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 8 years.
(7) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 3 years.
(9) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.