Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 3 years.
Correct Answer
$3864
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 4%
Time (t) = 3 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) = $3450 × 4% × 3
= $3450 ×4/100 × 3
= 3450 × 4 × 3/100
= 13800 × 3/100
= 41400/100
= $414
Thus, Simple Interest = $414
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 + $414
= $3864
Thus, Amount to be paid = $3864 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) = 4%
And, Time (t) = 3 years
Thus, Amount (A)
= $3450 + ($3450 × 4% × 3)
= $3450 + ($3450 ×4/100 × 3)
= $3450 + (3450 × 4 × 3/100)
= $3450 + (13800 × 3/100)
= $3450 + (41400/100)
= $3450 + $414 = $3864
Thus, Amount (A) to be paid = $3864 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 $3450, the simple interest in 1 year
= 4/100 × 3450
= 4 × 3450/100
= 13800/100 = $138
Thus, simple interest for 1 year = $138
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $138 × 3 = $414
Thus, Simple Interest (SI) = $414
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $414
= $3864
Thus, Amount to be paid = $3864 Answer
Similar Questions
(1) Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.
(3) Michael had to pay $3597 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(5) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.
(6) If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.
(8) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?
(9) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
(10) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.