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) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
(2) How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?
(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 7 years.
(4) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9512 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 8 years.
(6) If Matthew paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Mary had to pay $3324.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 7 years.
(9) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 7 years.
(10) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.