Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 8 years.
Correct Answer
$9810
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 8
= $5450 ×10/100 × 8
= 5450 × 10 × 8/100
= 54500 × 8/100
= 436000/100
= $4360
Thus, Simple Interest = $4360
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 + $4360
= $9810
Thus, Amount to be paid = $9810 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5450 + ($5450 × 10% × 8)
= $5450 + ($5450 ×10/100 × 8)
= $5450 + (5450 × 10 × 8/100)
= $5450 + (54500 × 8/100)
= $5450 + (436000/100)
= $5450 + $4360 = $9810
Thus, Amount (A) to be paid = $9810 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5450, the simple interest in 1 year
= 10/100 × 5450
= 10 × 5450/100
= 54500/100 = $545
Thus, simple interest for 1 year = $545
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $545 × 8 = $4360
Thus, Simple Interest (SI) = $4360
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $4360
= $9810
Thus, Amount to be paid = $9810 Answer
Similar Questions
(1) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.
(2) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.
(3) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(4) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 4 years.
(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 3 years.
(6) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.
(7) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(8) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 6% simple interest?
(9) In how much time a principal of $3150 will amount to $3276 at a simple interest of 2% per annum?
(10) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.