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) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 8 years.
(2) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.
(3) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?
(4) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.
(6) In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?
(7) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.
(9) If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) What amount does James have to pay after 5 years if he takes a loan of $3000 at 4% simple interest?