Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 3 years.
Correct Answer
$4485
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 10%
Time (t) = 3 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% × 3
= $3450 ×10/100 × 3
= 3450 × 10 × 3/100
= 34500 × 3/100
= 103500/100
= $1035
Thus, Simple Interest = $1035
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 + $1035
= $4485
Thus, Amount to be paid = $4485 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) = 3 years
Thus, Amount (A)
= $3450 + ($3450 × 10% × 3)
= $3450 + ($3450 ×10/100 × 3)
= $3450 + (3450 × 10 × 3/100)
= $3450 + (34500 × 3/100)
= $3450 + (103500/100)
= $3450 + $1035 = $4485
Thus, Amount (A) to be paid = $4485 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 3 years
= Simple interest for 1 year × 3
= $345 × 3 = $1035
Thus, Simple Interest (SI) = $1035
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $1035
= $4485
Thus, Amount to be paid = $4485 Answer
Similar Questions
(1) How much loan did Thomas borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6960 to clear it?
(2) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
(3) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 7 years.
(5) Susan had to pay $3978.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 3 years.
(7) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?
(8) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(10) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.