Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 3 years.
Correct Answer
$3811.5
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 7%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 3
= $3150 ×7/100 × 3
= 3150 × 7 × 3/100
= 22050 × 3/100
= 66150/100
= $661.5
Thus, Simple Interest = $661.5
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 + $661.5
= $3811.5
Thus, Amount to be paid = $3811.5 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) = 7%
And, Time (t) = 3 years
Thus, Amount (A)
= $3150 + ($3150 × 7% × 3)
= $3150 + ($3150 ×7/100 × 3)
= $3150 + (3150 × 7 × 3/100)
= $3150 + (22050 × 3/100)
= $3150 + (66150/100)
= $3150 + $661.5 = $3811.5
Thus, Amount (A) to be paid = $3811.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3150, the simple interest in 1 year
= 7/100 × 3150
= 7 × 3150/100
= 22050/100 = $220.5
Thus, simple interest for 1 year = $220.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $220.5 × 3 = $661.5
Thus, Simple Interest (SI) = $661.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $661.5
= $3811.5
Thus, Amount to be paid = $3811.5 Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?
(2) Kimberly had to pay $5208 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.
(4) John had to pay $3392 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
(6) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(7) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.
(8) How much loan did Betty borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7812.5 to clear it?
(9) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 4 years.
(10) 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.