Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 4 years.
Correct Answer
$4278
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 6%
Time (t) = 4 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% × 4
= $3450 ×6/100 × 4
= 3450 × 6 × 4/100
= 20700 × 4/100
= 82800/100
= $828
Thus, Simple Interest = $828
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 + $828
= $4278
Thus, Amount to be paid = $4278 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) = 4 years
Thus, Amount (A)
= $3450 + ($3450 × 6% × 4)
= $3450 + ($3450 ×6/100 × 4)
= $3450 + (3450 × 6 × 4/100)
= $3450 + (20700 × 4/100)
= $3450 + (82800/100)
= $3450 + $828 = $4278
Thus, Amount (A) to be paid = $4278 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 4 years
= Simple interest for 1 year × 4
= $207 × 4 = $828
Thus, Simple Interest (SI) = $828
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $828
= $4278
Thus, Amount to be paid = $4278 Answer
Similar Questions
(1) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 4 years.
(2) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(3) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?
(5) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.
(6) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.
(7) How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?
(8) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 6% simple interest?
(9) 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.
(10) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.