Question:
Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 7 years.
Correct Answer
$9046.5
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 9%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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) = $5550 × 9% × 7
= $5550 ×9/100 × 7
= 5550 × 9 × 7/100
= 49950 × 7/100
= 349650/100
= $3496.5
Thus, Simple Interest = $3496.5
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 = $5550 + $3496.5
= $9046.5
Thus, Amount to be paid = $9046.5 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 = $5550
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 7 years
Thus, Amount (A)
= $5550 + ($5550 × 9% × 7)
= $5550 + ($5550 ×9/100 × 7)
= $5550 + (5550 × 9 × 7/100)
= $5550 + (49950 × 7/100)
= $5550 + (349650/100)
= $5550 + $3496.5 = $9046.5
Thus, Amount (A) to be paid = $9046.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5550, the simple interest in 1 year
= 9/100 × 5550
= 9 × 5550/100
= 49950/100 = $499.5
Thus, simple interest for 1 year = $499.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $499.5 × 7 = $3496.5
Thus, Simple Interest (SI) = $3496.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $3496.5
= $9046.5
Thus, Amount to be paid = $9046.5 Answer
Similar Questions
(1) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 6% simple interest?
(2) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.
(4) How much loan did Matthew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7130 to clear it?
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 8 years.
(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 8 years.
(7) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?
(8) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.
(9) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.
(10) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12308 to clear the loan, then find the time period of the loan.