Question:
Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
Correct Answer
$7931
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 6%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 9
= $5150 ×6/100 × 9
= 5150 × 6 × 9/100
= 30900 × 9/100
= 278100/100
= $2781
Thus, Simple Interest = $2781
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 + $2781
= $7931
Thus, Amount to be paid = $7931 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) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5150 + ($5150 × 6% × 9)
= $5150 + ($5150 ×6/100 × 9)
= $5150 + (5150 × 6 × 9/100)
= $5150 + (30900 × 9/100)
= $5150 + (278100/100)
= $5150 + $2781 = $7931
Thus, Amount (A) to be paid = $7931 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5150, the simple interest in 1 year
= 6/100 × 5150
= 6 × 5150/100
= 30900/100 = $309
Thus, simple interest for 1 year = $309
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $309 × 9 = $2781
Thus, Simple Interest (SI) = $2781
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $2781
= $7931
Thus, Amount to be paid = $7931 Answer
Similar Questions
(1) 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.
(2) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.
(4) If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 7 years.
(6) If Michelle paid $5742 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 5% simple interest?
(8) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.
(10) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?