Question:
Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
Correct Answer
$7412
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 4%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 9
= $5450 ×4/100 × 9
= 5450 × 4 × 9/100
= 21800 × 9/100
= 196200/100
= $1962
Thus, Simple Interest = $1962
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 + $1962
= $7412
Thus, Amount to be paid = $7412 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) = 4%
And, Time (t) = 9 years
Thus, Amount (A)
= $5450 + ($5450 × 4% × 9)
= $5450 + ($5450 ×4/100 × 9)
= $5450 + (5450 × 4 × 9/100)
= $5450 + (21800 × 9/100)
= $5450 + (196200/100)
= $5450 + $1962 = $7412
Thus, Amount (A) to be paid = $7412 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5450, the simple interest in 1 year
= 4/100 × 5450
= 4 × 5450/100
= 21800/100 = $218
Thus, simple interest for 1 year = $218
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $218 × 9 = $1962
Thus, Simple Interest (SI) = $1962
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $1962
= $7412
Thus, Amount to be paid = $7412 Answer
Similar Questions
(1) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.
(2) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?
(3) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.
(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?
(5) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?
(7) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 7 years.
(8) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 9% simple interest?
(9) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(10) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.