Question:
What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?
Correct Answer
$5313
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 9%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 6
= $3450 ×9/100 × 6
= 3450 × 9 × 6/100
= 31050 × 6/100
= 186300/100
= $1863
Thus, Simple Interest = $1863
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 + $1863
= $5313
Thus, Amount to be paid = $5313 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) = 9%
And, Time (t) = 6 years
Thus, Amount (A)
= $3450 + ($3450 × 9% × 6)
= $3450 + ($3450 ×9/100 × 6)
= $3450 + (3450 × 9 × 6/100)
= $3450 + (31050 × 6/100)
= $3450 + (186300/100)
= $3450 + $1863 = $5313
Thus, Amount (A) to be paid = $5313 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $3450, the simple interest in 1 year
= 9/100 × 3450
= 9 × 3450/100
= 31050/100 = $310.5
Thus, simple interest for 1 year = $310.5
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $310.5 × 6 = $1863
Thus, Simple Interest (SI) = $1863
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $1863
= $5313
Thus, Amount to be paid = $5313 Answer
Similar Questions
(1) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 3 years.
(2) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 8 years.
(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 7 years.
(5) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 8 years.
(8) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.
(9) How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?
(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 3 years.