Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 7 years.
Correct Answer
$8502
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 8%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 7
= $5450 ×8/100 × 7
= 5450 × 8 × 7/100
= 43600 × 7/100
= 305200/100
= $3052
Thus, Simple Interest = $3052
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 + $3052
= $8502
Thus, Amount to be paid = $8502 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) = 8%
And, Time (t) = 7 years
Thus, Amount (A)
= $5450 + ($5450 × 8% × 7)
= $5450 + ($5450 ×8/100 × 7)
= $5450 + (5450 × 8 × 7/100)
= $5450 + (43600 × 7/100)
= $5450 + (305200/100)
= $5450 + $3052 = $8502
Thus, Amount (A) to be paid = $8502 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5450, the simple interest in 1 year
= 8/100 × 5450
= 8 × 5450/100
= 43600/100 = $436
Thus, simple interest for 1 year = $436
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $436 × 7 = $3052
Thus, Simple Interest (SI) = $3052
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $3052
= $8502
Thus, Amount to be paid = $8502 Answer
Similar Questions
(1) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 8 years.
(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.
(3) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(4) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 3 years.
(5) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(6) How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?
(7) How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?
(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 3 years.
(9) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(10) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.