Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.
Correct Answer
$8120.5
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 7%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 7
= $5450 ×7/100 × 7
= 5450 × 7 × 7/100
= 38150 × 7/100
= 267050/100
= $2670.5
Thus, Simple Interest = $2670.5
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 + $2670.5
= $8120.5
Thus, Amount to be paid = $8120.5 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) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5450 + ($5450 × 7% × 7)
= $5450 + ($5450 ×7/100 × 7)
= $5450 + (5450 × 7 × 7/100)
= $5450 + (38150 × 7/100)
= $5450 + (267050/100)
= $5450 + $2670.5 = $8120.5
Thus, Amount (A) to be paid = $8120.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5450, the simple interest in 1 year
= 7/100 × 5450
= 7 × 5450/100
= 38150/100 = $381.5
Thus, simple interest for 1 year = $381.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $381.5 × 7 = $2670.5
Thus, Simple Interest (SI) = $2670.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $2670.5
= $8120.5
Thus, Amount to be paid = $8120.5 Answer
Similar Questions
(1) How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?
(2) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(3) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 6% simple interest?
(4) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 4 years.
(5) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 4 years.
(7) How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?
(8) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?
(9) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 3 years.
(10) If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.