Question:
Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
Correct Answer
$8883.5
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 7%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 9
= $5450 ×7/100 × 9
= 5450 × 7 × 9/100
= 38150 × 9/100
= 343350/100
= $3433.5
Thus, Simple Interest = $3433.5
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 + $3433.5
= $8883.5
Thus, Amount to be paid = $8883.5 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) = 7%
And, Time (t) = 9 years
Thus, Amount (A)
= $5450 + ($5450 × 7% × 9)
= $5450 + ($5450 ×7/100 × 9)
= $5450 + (5450 × 7 × 9/100)
= $5450 + (38150 × 9/100)
= $5450 + (343350/100)
= $5450 + $3433.5 = $8883.5
Thus, Amount (A) to be paid = $8883.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5450, the simple interest in 1 year
= 7/100 × 5450
= 7 × 5450/100
= 38150/100 = $381.5
Thus, simple interest for 1 year = $381.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $381.5 × 9 = $3433.5
Thus, Simple Interest (SI) = $3433.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $3433.5
= $8883.5
Thus, Amount to be paid = $8883.5 Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?
(2) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?
(3) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8797.5 to clear it?
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.
(5) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.
(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 4 years.
(8) Robert had to pay $3472 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?