Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 7 years.
Correct Answer
$7739
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 6%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 7
= $5450 ×6/100 × 7
= 5450 × 6 × 7/100
= 32700 × 7/100
= 228900/100
= $2289
Thus, Simple Interest = $2289
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 + $2289
= $7739
Thus, Amount to be paid = $7739 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) = 6%
And, Time (t) = 7 years
Thus, Amount (A)
= $5450 + ($5450 × 6% × 7)
= $5450 + ($5450 ×6/100 × 7)
= $5450 + (5450 × 6 × 7/100)
= $5450 + (32700 × 7/100)
= $5450 + (228900/100)
= $5450 + $2289 = $7739
Thus, Amount (A) to be paid = $7739 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5450, the simple interest in 1 year
= 6/100 × 5450
= 6 × 5450/100
= 32700/100 = $327
Thus, simple interest for 1 year = $327
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $327 × 7 = $2289
Thus, Simple Interest (SI) = $2289
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $2289
= $7739
Thus, Amount to be paid = $7739 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.
(2) How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?
(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 3 years.
(4) If Betty paid $5100 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?
(6) Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 8 years.
(8) What amount does John have to pay after 6 years if he takes a loan of $3200 at 4% simple interest?
(9) If Joseph paid $4292 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?