Question:
Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.
Correct Answer
$10545
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 10%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 9
= $5550 ×10/100 × 9
= 5550 × 10 × 9/100
= 55500 × 9/100
= 499500/100
= $4995
Thus, Simple Interest = $4995
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 + $4995
= $10545
Thus, Amount to be paid = $10545 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) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5550 + ($5550 × 10% × 9)
= $5550 + ($5550 ×10/100 × 9)
= $5550 + (5550 × 10 × 9/100)
= $5550 + (55500 × 9/100)
= $5550 + (499500/100)
= $5550 + $4995 = $10545
Thus, Amount (A) to be paid = $10545 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5550, the simple interest in 1 year
= 10/100 × 5550
= 10 × 5550/100
= 55500/100 = $555
Thus, simple interest for 1 year = $555
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $555 × 9 = $4995
Thus, Simple Interest (SI) = $4995
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $4995
= $10545
Thus, Amount to be paid = $10545 Answer
Similar Questions
(1) Margaret had to pay $4611 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 7 years.
(3) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 9% simple interest?
(4) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 3 years.
(5) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(6) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?
(7) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 9% simple interest?
(8) If Patricia borrowed $3150 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(9) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 7 years.