Question:
Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.
Correct Answer
$6540
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 2%
Time (t) = 10 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% × 10
= $5450 ×2/100 × 10
= 5450 × 2 × 10/100
= 10900 × 10/100
= 109000/100
= $1090
Thus, Simple Interest = $1090
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 + $1090
= $6540
Thus, Amount to be paid = $6540 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) = 10 years
Thus, Amount (A)
= $5450 + ($5450 × 2% × 10)
= $5450 + ($5450 ×2/100 × 10)
= $5450 + (5450 × 2 × 10/100)
= $5450 + (10900 × 10/100)
= $5450 + (109000/100)
= $5450 + $1090 = $6540
Thus, Amount (A) to be paid = $6540 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 10 years
= Simple interest for 1 year × 10
= $109 × 10 = $1090
Thus, Simple Interest (SI) = $1090
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $1090
= $6540
Thus, Amount to be paid = $6540 Answer
Similar Questions
(1) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 2% simple interest?
(2) Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.
(4) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.
(5) 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.
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 7 years.
(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
(8) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 8 years.
(9) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $10000 to clear the loan, then find the time period of the loan.
(10) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.