Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 7 years.
Correct Answer
$8502
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 8%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 7
= $5450 ×8/100 × 7
= 5450 × 8 × 7/100
= 43600 × 7/100
= 305200/100
= $3052
Thus, Simple Interest = $3052
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 + $3052
= $8502
Thus, Amount to be paid = $8502 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) = 8%
And, Time (t) = 7 years
Thus, Amount (A)
= $5450 + ($5450 × 8% × 7)
= $5450 + ($5450 ×8/100 × 7)
= $5450 + (5450 × 8 × 7/100)
= $5450 + (43600 × 7/100)
= $5450 + (305200/100)
= $5450 + $3052 = $8502
Thus, Amount (A) to be paid = $8502 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5450, the simple interest in 1 year
= 8/100 × 5450
= 8 × 5450/100
= 43600/100 = $436
Thus, simple interest for 1 year = $436
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $436 × 7 = $3052
Thus, Simple Interest (SI) = $3052
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $3052
= $8502
Thus, Amount to be paid = $8502 Answer
Similar Questions
(1) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 8% simple interest?
(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.
(3) If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.
(6) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.
(7) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 3 years.
(9) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.
(10) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.