Question:
Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.
Correct Answer
$11100
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 10%
Time (t) = 10 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% × 10
= $5550 ×10/100 × 10
= 5550 × 10 × 10/100
= 55500 × 10/100
= 555000/100
= $5550
Thus, Simple Interest = $5550
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 + $5550
= $11100
Thus, Amount to be paid = $11100 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) = 10 years
Thus, Amount (A)
= $5550 + ($5550 × 10% × 10)
= $5550 + ($5550 ×10/100 × 10)
= $5550 + (5550 × 10 × 10/100)
= $5550 + (55500 × 10/100)
= $5550 + (555000/100)
= $5550 + $5550 = $11100
Thus, Amount (A) to be paid = $11100 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 10 years
= Simple interest for 1 year × 10
= $555 × 10 = $5550
Thus, Simple Interest (SI) = $5550
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $5550
= $11100
Thus, Amount to be paid = $11100 Answer
Similar Questions
(1) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 8% simple interest?
(2) 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.
(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.
(4) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.
(5) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(6) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if James borrowed a sum of $3000 at a 8% simple interest?
(8) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(9) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 5% simple interest?