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) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 8 years.
(2) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(3) What amount does William have to pay after 5 years if he takes a loan of $3500 at 10% simple interest?
(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 8% simple interest?
(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 8 years.
(7) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(9) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(10) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.