Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 years.
Correct Answer
$3528
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 3%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 4
= $3150 ×3/100 × 4
= 3150 × 3 × 4/100
= 9450 × 4/100
= 37800/100
= $378
Thus, Simple Interest = $378
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 + $378
= $3528
Thus, Amount to be paid = $3528 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) = 3%
And, Time (t) = 4 years
Thus, Amount (A)
= $3150 + ($3150 × 3% × 4)
= $3150 + ($3150 ×3/100 × 4)
= $3150 + (3150 × 3 × 4/100)
= $3150 + (9450 × 4/100)
= $3150 + (37800/100)
= $3150 + $378 = $3528
Thus, Amount (A) to be paid = $3528 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3150, the simple interest in 1 year
= 3/100 × 3150
= 3 × 3150/100
= 9450/100 = $94.5
Thus, simple interest for 1 year = $94.5
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $94.5 × 4 = $378
Thus, Simple Interest (SI) = $378
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $378
= $3528
Thus, Amount to be paid = $3528 Answer
Similar Questions
(1) How much loan did Michelle borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7992.5 to clear it?
(2) William had to pay $3920 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 8 years.
(4) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(5) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 3 years.
(6) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
(7) How much loan did Richard borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6160 to clear it?
(8) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 3% simple interest.
(9) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.