Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 8 years.
Correct Answer
$8066
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 6%
Time (t) = 8 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% × 8
= $5450 ×6/100 × 8
= 5450 × 6 × 8/100
= 32700 × 8/100
= 261600/100
= $2616
Thus, Simple Interest = $2616
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 + $2616
= $8066
Thus, Amount to be paid = $8066 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) = 8 years
Thus, Amount (A)
= $5450 + ($5450 × 6% × 8)
= $5450 + ($5450 ×6/100 × 8)
= $5450 + (5450 × 6 × 8/100)
= $5450 + (32700 × 8/100)
= $5450 + (261600/100)
= $5450 + $2616 = $8066
Thus, Amount (A) to be paid = $8066 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 8 years
= Simple interest for 1 year × 8
= $327 × 8 = $2616
Thus, Simple Interest (SI) = $2616
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $2616
= $8066
Thus, Amount to be paid = $8066 Answer
Similar Questions
(1) What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?
(2) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $10498 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.
(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.
(5) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.
(6) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(7) If Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(8) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 8% simple interest?
(10) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.