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 Jessica have to pay after 6 years if he takes a loan of $3750 at 4% simple interest?
(2) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.
(3) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 8% simple interest?
(5) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(6) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 8% simple interest?
(7) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?
(8) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.
(9) If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.