Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 3 years.
Correct Answer
$3622.5
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 5%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 3
= $3150 ×5/100 × 3
= 3150 × 5 × 3/100
= 15750 × 3/100
= 47250/100
= $472.5
Thus, Simple Interest = $472.5
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 + $472.5
= $3622.5
Thus, Amount to be paid = $3622.5 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) = 5%
And, Time (t) = 3 years
Thus, Amount (A)
= $3150 + ($3150 × 5% × 3)
= $3150 + ($3150 ×5/100 × 3)
= $3150 + (3150 × 5 × 3/100)
= $3150 + (15750 × 3/100)
= $3150 + (47250/100)
= $3150 + $472.5 = $3622.5
Thus, Amount (A) to be paid = $3622.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3150, the simple interest in 1 year
= 5/100 × 3150
= 5 × 3150/100
= 15750/100 = $157.5
Thus, simple interest for 1 year = $157.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $157.5 × 3 = $472.5
Thus, Simple Interest (SI) = $472.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $472.5
= $3622.5
Thus, Amount to be paid = $3622.5 Answer
Similar Questions
(1) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(2) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 4 years.
(4) If Karen borrowed $3950 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.
(7) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.
(8) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?
(9) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 3 years.
(10) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.