Question:
Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
Correct Answer
$8393
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 6%
Time (t) = 9 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% × 9
= $5450 ×6/100 × 9
= 5450 × 6 × 9/100
= 32700 × 9/100
= 294300/100
= $2943
Thus, Simple Interest = $2943
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 + $2943
= $8393
Thus, Amount to be paid = $8393 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) = 9 years
Thus, Amount (A)
= $5450 + ($5450 × 6% × 9)
= $5450 + ($5450 ×6/100 × 9)
= $5450 + (5450 × 6 × 9/100)
= $5450 + (32700 × 9/100)
= $5450 + (294300/100)
= $5450 + $2943 = $8393
Thus, Amount (A) to be paid = $8393 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 9 years
= Simple interest for 1 year × 9
= $327 × 9 = $2943
Thus, Simple Interest (SI) = $2943
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $2943
= $8393
Thus, Amount to be paid = $8393 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 3 years.
(3) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.
(4) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(5) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.
(6) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?
(7) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 4% simple interest?
(8) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.
(10) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 4 years.