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) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.
(2) Jennifer had to pay $3640 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 8 years.
(5) In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?
(6) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.
(8) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.
(9) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 7 years.
(10) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.