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 Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 4 years.
(3) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?
(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?
(5) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6888 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if William borrowed a sum of $3250 at a 10% simple interest?
(7) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 6% simple interest?
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 8 years.
(9) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.
(10) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.