Question:
Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.
Correct Answer
$8325
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 5%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 10
= $5550 ×5/100 × 10
= 5550 × 5 × 10/100
= 27750 × 10/100
= 277500/100
= $2775
Thus, Simple Interest = $2775
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 + $2775
= $8325
Thus, Amount to be paid = $8325 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) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5550 + ($5550 × 5% × 10)
= $5550 + ($5550 ×5/100 × 10)
= $5550 + (5550 × 5 × 10/100)
= $5550 + (27750 × 10/100)
= $5550 + (277500/100)
= $5550 + $2775 = $8325
Thus, Amount (A) to be paid = $8325 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5550, the simple interest in 1 year
= 5/100 × 5550
= 5 × 5550/100
= 27750/100 = $277.5
Thus, simple interest for 1 year = $277.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $277.5 × 10 = $2775
Thus, Simple Interest (SI) = $2775
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $2775
= $8325
Thus, Amount to be paid = $8325 Answer
Similar Questions
(1) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
(2) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.
(4) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(5) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3100 will amount to $3348 at a simple interest of 4% per annum?
(7) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.
(8) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 4 years.
(9) If Robert borrowed $3100 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?