Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 7 years.
Correct Answer
$7357.5
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 5%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 7
= $5450 ×5/100 × 7
= 5450 × 5 × 7/100
= 27250 × 7/100
= 190750/100
= $1907.5
Thus, Simple Interest = $1907.5
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 + $1907.5
= $7357.5
Thus, Amount to be paid = $7357.5 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) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5450 + ($5450 × 5% × 7)
= $5450 + ($5450 ×5/100 × 7)
= $5450 + (5450 × 5 × 7/100)
= $5450 + (27250 × 7/100)
= $5450 + (190750/100)
= $5450 + $1907.5 = $7357.5
Thus, Amount (A) to be paid = $7357.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5450, the simple interest in 1 year
= 5/100 × 5450
= 5 × 5450/100
= 27250/100 = $272.5
Thus, simple interest for 1 year = $272.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $272.5 × 7 = $1907.5
Thus, Simple Interest (SI) = $1907.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $1907.5
= $7357.5
Thus, Amount to be paid = $7357.5 Answer
Similar Questions
(1) If Kimberly paid $5022 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(3) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 8% simple interest?
(4) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.
(5) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 7 years.
(7) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.
(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 7 years.
(10) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?