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 after 9 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.
(2) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.
(3) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 9% simple interest?
(5) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.
(6) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.
(7) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
(8) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?
(9) If Emily paid $5130 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) How much loan did Emily borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8100 to clear it?