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) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?
(2) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(3) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.
(4) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?
(5) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?
(6) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) What amount does William have to pay after 5 years if he takes a loan of $3500 at 8% simple interest?
(8) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 6% simple interest?
(9) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.
(10) How much loan did Ashley borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8187.5 to clear it?