Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 4 years.
Correct Answer
$3864
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 3%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 4
= $3450 ×3/100 × 4
= 3450 × 3 × 4/100
= 10350 × 4/100
= 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) = 3%
And, Time (t) = 4 years
Thus, Amount (A)
= $3450 + ($3450 × 3% × 4)
= $3450 + ($3450 ×3/100 × 4)
= $3450 + (3450 × 3 × 4/100)
= $3450 + (10350 × 4/100)
= $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 = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3450, the simple interest in 1 year
= 3/100 × 3450
= 3 × 3450/100
= 10350/100 = $103.5
Thus, simple interest for 1 year = $103.5
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $103.5 × 4 = $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) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 7% simple interest?
(2) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.
(3) David had to pay $3604 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.
(7) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?
(8) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.
(10) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.