Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 8 years.
Correct Answer
$6758
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 3%
Time (t) = 8 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% × 8
= $5450 ×3/100 × 8
= 5450 × 3 × 8/100
= 16350 × 8/100
= 130800/100
= $1308
Thus, Simple Interest = $1308
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 + $1308
= $6758
Thus, Amount to be paid = $6758 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) = 8 years
Thus, Amount (A)
= $5450 + ($5450 × 3% × 8)
= $5450 + ($5450 ×3/100 × 8)
= $5450 + (5450 × 3 × 8/100)
= $5450 + (16350 × 8/100)
= $5450 + (130800/100)
= $5450 + $1308 = $6758
Thus, Amount (A) to be paid = $6758 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 8 years
= Simple interest for 1 year × 8
= $163.5 × 8 = $1308
Thus, Simple Interest (SI) = $1308
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $1308
= $6758
Thus, Amount to be paid = $6758 Answer
Similar Questions
(1) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 8 years.
(3) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
(4) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.
(6) 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?
(7) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 3% simple interest?
(8) Emily had to pay $5035 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.
(10) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.