Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 8 years.
Correct Answer
$6322
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 2%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 8
= $5450 ×2/100 × 8
= 5450 × 2 × 8/100
= 10900 × 8/100
= 87200/100
= $872
Thus, Simple Interest = $872
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 + $872
= $6322
Thus, Amount to be paid = $6322 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) = 2%
And, Time (t) = 8 years
Thus, Amount (A)
= $5450 + ($5450 × 2% × 8)
= $5450 + ($5450 ×2/100 × 8)
= $5450 + (5450 × 2 × 8/100)
= $5450 + (10900 × 8/100)
= $5450 + (87200/100)
= $5450 + $872 = $6322
Thus, Amount (A) to be paid = $6322 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5450, the simple interest in 1 year
= 2/100 × 5450
= 2 × 5450/100
= 10900/100 = $109
Thus, simple interest for 1 year = $109
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $109 × 8 = $872
Thus, Simple Interest (SI) = $872
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $872
= $6322
Thus, Amount to be paid = $6322 Answer
Similar Questions
(1) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 7 years.
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 4 years.
(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.
(4) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.
(5) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 3% simple interest?
(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 3 years.
(7) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(8) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 6% simple interest?
(9) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?
(10) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?