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) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(3) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.
(5) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 7 years.
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 7 years.
(7) If Barbara borrowed $3550 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 8 years.
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.
(10) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.