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) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 6% simple interest?
(2) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9248 to clear the loan, then find the time period of the loan.
(3) How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?
(4) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.
(5) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.
(6) If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(8) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 10% simple interest?
(10) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 4 years.