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 Michael borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6095 to clear it?
(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.
(3) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.
(4) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 7% simple interest?
(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.
(7) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 7% simple interest?
(8) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
(9) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 7 years.