Question:
Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.
Correct Answer
$7085
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 3%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 10
= $5450 ×3/100 × 10
= 5450 × 3 × 10/100
= 16350 × 10/100
= 163500/100
= $1635
Thus, Simple Interest = $1635
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 + $1635
= $7085
Thus, Amount to be paid = $7085 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) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5450 + ($5450 × 3% × 10)
= $5450 + ($5450 ×3/100 × 10)
= $5450 + (5450 × 3 × 10/100)
= $5450 + (16350 × 10/100)
= $5450 + (163500/100)
= $5450 + $1635 = $7085
Thus, Amount (A) to be paid = $7085 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5450, the simple interest in 1 year
= 3/100 × 5450
= 3 × 5450/100
= 16350/100 = $163.5
Thus, simple interest for 1 year = $163.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $163.5 × 10 = $1635
Thus, Simple Interest (SI) = $1635
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $1635
= $7085
Thus, Amount to be paid = $7085 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.
(2) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(3) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.
(4) How much loan did Deborah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8567.5 to clear it?
(5) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.
(6) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 10% simple interest?
(8) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 4 years.
(9) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 4 years.
(10) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.