Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 7 years.
Correct Answer
$6213
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 2%
Time (t) = 7 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% × 7
= $5450 ×2/100 × 7
= 5450 × 2 × 7/100
= 10900 × 7/100
= 76300/100
= $763
Thus, Simple Interest = $763
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 + $763
= $6213
Thus, Amount to be paid = $6213 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) = 7 years
Thus, Amount (A)
= $5450 + ($5450 × 2% × 7)
= $5450 + ($5450 ×2/100 × 7)
= $5450 + (5450 × 2 × 7/100)
= $5450 + (10900 × 7/100)
= $5450 + (76300/100)
= $5450 + $763 = $6213
Thus, Amount (A) to be paid = $6213 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 7 years
= Simple interest for 1 year × 7
= $109 × 7 = $763
Thus, Simple Interest (SI) = $763
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $763
= $6213
Thus, Amount to be paid = $6213 Answer
Similar Questions
(1) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 8 years.
(3) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.
(4) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
(6) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
(7) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.
(8) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.
(9) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?
(10) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.