Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 4 years.
Correct Answer
$4692
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 9%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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) = $3450 × 9% × 4
= $3450 ×9/100 × 4
= 3450 × 9 × 4/100
= 31050 × 4/100
= 124200/100
= $1242
Thus, Simple Interest = $1242
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 = $3450 + $1242
= $4692
Thus, Amount to be paid = $4692 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 = $3450
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 4 years
Thus, Amount (A)
= $3450 + ($3450 × 9% × 4)
= $3450 + ($3450 ×9/100 × 4)
= $3450 + (3450 × 9 × 4/100)
= $3450 + (31050 × 4/100)
= $3450 + (124200/100)
= $3450 + $1242 = $4692
Thus, Amount (A) to be paid = $4692 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $3450, the simple interest in 1 year
= 9/100 × 3450
= 9 × 3450/100
= 31050/100 = $310.5
Thus, simple interest for 1 year = $310.5
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $310.5 × 4 = $1242
Thus, Simple Interest (SI) = $1242
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $1242
= $4692
Thus, Amount to be paid = $4692 Answer
Similar Questions
(1) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.
(2) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7152 to clear the loan, then find the time period of the loan.
(3) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 3 years.
(6) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.
(7) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
(8) If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.
(10) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.