Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 4 years.
Correct Answer
$4410
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 10%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 4
= $3150 ×10/100 × 4
= 3150 × 10 × 4/100
= 31500 × 4/100
= 126000/100
= $1260
Thus, Simple Interest = $1260
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 + $1260
= $4410
Thus, Amount to be paid = $4410 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) = 10%
And, Time (t) = 4 years
Thus, Amount (A)
= $3150 + ($3150 × 10% × 4)
= $3150 + ($3150 ×10/100 × 4)
= $3150 + (3150 × 10 × 4/100)
= $3150 + (31500 × 4/100)
= $3150 + (126000/100)
= $3150 + $1260 = $4410
Thus, Amount (A) to be paid = $4410 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3150, the simple interest in 1 year
= 10/100 × 3150
= 10 × 3150/100
= 31500/100 = $315
Thus, simple interest for 1 year = $315
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $315 × 4 = $1260
Thus, Simple Interest (SI) = $1260
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $1260
= $4410
Thus, Amount to be paid = $4410 Answer
Similar Questions
(1) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 5% simple interest?
(2) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 2% simple interest?
(4) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9676 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 8 years.
(6) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 5% simple interest?
(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 7 years.
(8) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 8 years.
(10) If Linda paid $4020 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.