Question:
Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
Correct Answer
$7412
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 4%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 9
= $5450 ×4/100 × 9
= 5450 × 4 × 9/100
= 21800 × 9/100
= 196200/100
= $1962
Thus, Simple Interest = $1962
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 + $1962
= $7412
Thus, Amount to be paid = $7412 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) = 4%
And, Time (t) = 9 years
Thus, Amount (A)
= $5450 + ($5450 × 4% × 9)
= $5450 + ($5450 ×4/100 × 9)
= $5450 + (5450 × 4 × 9/100)
= $5450 + (21800 × 9/100)
= $5450 + (196200/100)
= $5450 + $1962 = $7412
Thus, Amount (A) to be paid = $7412 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5450, the simple interest in 1 year
= 4/100 × 5450
= 4 × 5450/100
= 21800/100 = $218
Thus, simple interest for 1 year = $218
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $218 × 9 = $1962
Thus, Simple Interest (SI) = $1962
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $1962
= $7412
Thus, Amount to be paid = $7412 Answer
Similar Questions
(1) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
(2) How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?
(3) How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?
(4) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.
(5) Kenneth had to pay $5300 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?
(7) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?
(9) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 7 years.