Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 3 years.
Correct Answer
$4174.5
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 7%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 3
= $3450 ×7/100 × 3
= 3450 × 7 × 3/100
= 24150 × 3/100
= 72450/100
= $724.5
Thus, Simple Interest = $724.5
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 + $724.5
= $4174.5
Thus, Amount to be paid = $4174.5 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) = 7%
And, Time (t) = 3 years
Thus, Amount (A)
= $3450 + ($3450 × 7% × 3)
= $3450 + ($3450 ×7/100 × 3)
= $3450 + (3450 × 7 × 3/100)
= $3450 + (24150 × 3/100)
= $3450 + (72450/100)
= $3450 + $724.5 = $4174.5
Thus, Amount (A) to be paid = $4174.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3450, the simple interest in 1 year
= 7/100 × 3450
= 7 × 3450/100
= 24150/100 = $241.5
Thus, simple interest for 1 year = $241.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $241.5 × 3 = $724.5
Thus, Simple Interest (SI) = $724.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $724.5
= $4174.5
Thus, Amount to be paid = $4174.5 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
(2) How much loan did Steven borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7920 to clear it?
(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 2% simple interest?
(4) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(5) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11403 to clear the loan, then find the time period of the loan.
(6) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.
(7) What amount does William have to pay after 5 years if he takes a loan of $3500 at 5% simple interest?
(8) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.
(9) Sandra had to pay $4717 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7602 to clear the loan, then find the time period of the loan.