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) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 4 years.
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.
(3) How much loan did Sarah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6435 to clear it?
(4) Donna had to pay $5141 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 8 years.
(6) Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.
(8) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 7% simple interest?
(9) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(10) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10860 to clear the loan, then find the time period of the loan.