Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.
Correct Answer
$4071
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 6%
Time (t) = 3 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) = $3450 × 6% × 3
= $3450 ×6/100 × 3
= 3450 × 6 × 3/100
= 20700 × 3/100
= 62100/100
= $621
Thus, Simple Interest = $621
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 + $621
= $4071
Thus, Amount to be paid = $4071 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) = 6%
And, Time (t) = 3 years
Thus, Amount (A)
= $3450 + ($3450 × 6% × 3)
= $3450 + ($3450 ×6/100 × 3)
= $3450 + (3450 × 6 × 3/100)
= $3450 + (20700 × 3/100)
= $3450 + (62100/100)
= $3450 + $621 = $4071
Thus, Amount (A) to be paid = $4071 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 $3450, the simple interest in 1 year
= 6/100 × 3450
= 6 × 3450/100
= 20700/100 = $207
Thus, simple interest for 1 year = $207
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $207 × 3 = $621
Thus, Simple Interest (SI) = $621
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $621
= $4071
Thus, Amount to be paid = $4071 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $5848 to clear the loan, then find the time period of the loan.
(2) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 4 years.
(4) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.
(5) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 4 years.
(7) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 8 years.
(9) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?
(10) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.