Question:
What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 9% simple interest?
Correct Answer
$4851
Solution And Explanation
Solution
Given,
Principal (P) = $3150
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) = $3150 × 9% × 6
= $3150 ×9/100 × 6
= 3150 × 9 × 6/100
= 28350 × 6/100
= 170100/100
= $1701
Thus, Simple Interest = $1701
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 = $3150 + $1701
= $4851
Thus, Amount to be paid = $4851 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 = $3150
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 6 years
Thus, Amount (A)
= $3150 + ($3150 × 9% × 6)
= $3150 + ($3150 ×9/100 × 6)
= $3150 + (3150 × 9 × 6/100)
= $3150 + (28350 × 6/100)
= $3150 + (170100/100)
= $3150 + $1701 = $4851
Thus, Amount (A) to be paid = $4851 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 $3150, the simple interest in 1 year
= 9/100 × 3150
= 9 × 3150/100
= 28350/100 = $283.5
Thus, simple interest for 1 year = $283.5
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $283.5 × 6 = $1701
Thus, Simple Interest (SI) = $1701
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $1701
= $4851
Thus, Amount to be paid = $4851 Answer
Similar Questions
(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 8 years.
(2) What amount does James have to pay after 5 years if he takes a loan of $3000 at 8% simple interest?
(3) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
(4) Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 4% simple interest?
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 7 years.
(9) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 7 years.
(10) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.