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) If Steven paid $5336 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.
(3) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(4) What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?
(5) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?
(6) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 3 years.
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 7 years.
(8) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(9) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.
(10) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.