Question:
Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
Correct Answer
$8883.5
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 7%
Time (t) = 9 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% × 9
= $5450 ×7/100 × 9
= 5450 × 7 × 9/100
= 38150 × 9/100
= 343350/100
= $3433.5
Thus, Simple Interest = $3433.5
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 + $3433.5
= $8883.5
Thus, Amount to be paid = $8883.5 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) = 9 years
Thus, Amount (A)
= $5450 + ($5450 × 7% × 9)
= $5450 + ($5450 ×7/100 × 9)
= $5450 + (5450 × 7 × 9/100)
= $5450 + (38150 × 9/100)
= $5450 + (343350/100)
= $5450 + $3433.5 = $8883.5
Thus, Amount (A) to be paid = $8883.5 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 9 years
= Simple interest for 1 year × 9
= $381.5 × 9 = $3433.5
Thus, Simple Interest (SI) = $3433.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $3433.5
= $8883.5
Thus, Amount to be paid = $8883.5 Answer
Similar Questions
(1) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(2) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?
(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.
(4) In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?
(5) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
(6) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?
(7) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 7% simple interest?
(8) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 7 years.
(10) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?