Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 4 years.
Correct Answer
$4830
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 10%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 4
= $3450 ×10/100 × 4
= 3450 × 10 × 4/100
= 34500 × 4/100
= 138000/100
= $1380
Thus, Simple Interest = $1380
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 + $1380
= $4830
Thus, Amount to be paid = $4830 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) = 10%
And, Time (t) = 4 years
Thus, Amount (A)
= $3450 + ($3450 × 10% × 4)
= $3450 + ($3450 ×10/100 × 4)
= $3450 + (3450 × 10 × 4/100)
= $3450 + (34500 × 4/100)
= $3450 + (138000/100)
= $3450 + $1380 = $4830
Thus, Amount (A) to be paid = $4830 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3450, the simple interest in 1 year
= 10/100 × 3450
= 10 × 3450/100
= 34500/100 = $345
Thus, simple interest for 1 year = $345
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $345 × 4 = $1380
Thus, Simple Interest (SI) = $1380
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $1380
= $4830
Thus, Amount to be paid = $4830 Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.
(2) William had to pay $3710 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.
(4) Donna had to pay $5432 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 7 years.
(6) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 8 years.
(8) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 3 years.
(9) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.
(10) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $8704 to clear the loan, then find the time period of the loan.