Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 7 years.
Correct Answer
$6976
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 4%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 7
= $5450 ×4/100 × 7
= 5450 × 4 × 7/100
= 21800 × 7/100
= 152600/100
= $1526
Thus, Simple Interest = $1526
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 + $1526
= $6976
Thus, Amount to be paid = $6976 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) = 4%
And, Time (t) = 7 years
Thus, Amount (A)
= $5450 + ($5450 × 4% × 7)
= $5450 + ($5450 ×4/100 × 7)
= $5450 + (5450 × 4 × 7/100)
= $5450 + (21800 × 7/100)
= $5450 + (152600/100)
= $5450 + $1526 = $6976
Thus, Amount (A) to be paid = $6976 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5450, the simple interest in 1 year
= 4/100 × 5450
= 4 × 5450/100
= 21800/100 = $218
Thus, simple interest for 1 year = $218
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $218 × 7 = $1526
Thus, Simple Interest (SI) = $1526
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $1526
= $6976
Thus, Amount to be paid = $6976 Answer
Similar Questions
(1) If Elizabeth paid $4140 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(3) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.
(5) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
(6) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.
(9) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 9% simple interest?
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 8 years.