Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.
Correct Answer
$8938
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 8%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 8
= $5450 ×8/100 × 8
= 5450 × 8 × 8/100
= 43600 × 8/100
= 348800/100
= $3488
Thus, Simple Interest = $3488
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 + $3488
= $8938
Thus, Amount to be paid = $8938 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) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5450 + ($5450 × 8% × 8)
= $5450 + ($5450 ×8/100 × 8)
= $5450 + (5450 × 8 × 8/100)
= $5450 + (43600 × 8/100)
= $5450 + (348800/100)
= $5450 + $3488 = $8938
Thus, Amount (A) to be paid = $8938 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5450, the simple interest in 1 year
= 8/100 × 5450
= 8 × 5450/100
= 43600/100 = $436
Thus, simple interest for 1 year = $436
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $436 × 8 = $3488
Thus, Simple Interest (SI) = $3488
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $3488
= $8938
Thus, Amount to be paid = $8938 Answer
Similar Questions
(1) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
(2) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(3) If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) What amount does William have to pay after 5 years if he takes a loan of $3500 at 2% simple interest?
(5) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?
(6) How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?
(7) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 3 years.
(8) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 4 years.
(10) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $8400 to clear the loan, then find the time period of the loan.