Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 7 years.
Correct Answer
$6231.5
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 3%
Time (t) = 7 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) = $5150 × 3% × 7
= $5150 ×3/100 × 7
= 5150 × 3 × 7/100
= 15450 × 7/100
= 108150/100
= $1081.5
Thus, Simple Interest = $1081.5
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 = $5150 + $1081.5
= $6231.5
Thus, Amount to be paid = $6231.5 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 = $5150
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 7 years
Thus, Amount (A)
= $5150 + ($5150 × 3% × 7)
= $5150 + ($5150 ×3/100 × 7)
= $5150 + (5150 × 3 × 7/100)
= $5150 + (15450 × 7/100)
= $5150 + (108150/100)
= $5150 + $1081.5 = $6231.5
Thus, Amount (A) to be paid = $6231.5 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 $5150, the simple interest in 1 year
= 3/100 × 5150
= 3 × 5150/100
= 15450/100 = $154.5
Thus, simple interest for 1 year = $154.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $154.5 × 7 = $1081.5
Thus, Simple Interest (SI) = $1081.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $1081.5
= $6231.5
Thus, Amount to be paid = $6231.5 Answer
Similar Questions
(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 8 years.
(2) How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 4 years.
(4) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?
(5) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.
(8) If David borrowed $3400 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(9) How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?
(10) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.