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) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 3 years.
(3) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(4) How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?
(5) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.
(6) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(7) What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?
(8) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?
(9) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.
(10) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 2% simple interest?