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) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?
(2) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 6% simple interest?
(3) How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?
(4) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 3 years.
(6) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(7) If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.
(9) If Patricia paid $3402 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?