Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 8 years.
Correct Answer
$8502
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 7%
Time (t) = 8 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% × 8
= $5450 ×7/100 × 8
= 5450 × 7 × 8/100
= 38150 × 8/100
= 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) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5450 + ($5450 × 7% × 8)
= $5450 + ($5450 ×7/100 × 8)
= $5450 + (5450 × 7 × 8/100)
= $5450 + (38150 × 8/100)
= $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 = 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 8 years
= Simple interest for 1 year × 8
= $381.5 × 8 = $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) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 3 years.
(2) If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9050 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.
(5) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 4 years.
(7) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 8% simple interest?
(9) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.
(10) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 3% simple interest?