Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.
Correct Answer
$4158
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 8%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 4
= $3150 ×8/100 × 4
= 3150 × 8 × 4/100
= 25200 × 4/100
= 100800/100
= $1008
Thus, Simple Interest = $1008
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 + $1008
= $4158
Thus, Amount to be paid = $4158 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) = 8%
And, Time (t) = 4 years
Thus, Amount (A)
= $3150 + ($3150 × 8% × 4)
= $3150 + ($3150 ×8/100 × 4)
= $3150 + (3150 × 8 × 4/100)
= $3150 + (25200 × 4/100)
= $3150 + (100800/100)
= $3150 + $1008 = $4158
Thus, Amount (A) to be paid = $4158 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $3150, the simple interest in 1 year
= 8/100 × 3150
= 8 × 3150/100
= 25200/100 = $252
Thus, simple interest for 1 year = $252
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $252 × 4 = $1008
Thus, Simple Interest (SI) = $1008
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $1008
= $4158
Thus, Amount to be paid = $4158 Answer
Similar Questions
(1) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 6% simple interest?
(2) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.
(4) How much loan did Mark borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7680 to clear it?
(5) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(6) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 10% simple interest?
(7) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 7 years.
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 8 years.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 8 years.
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 7 years.