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 if Patricia borrowed a sum of $3150 at 2% simple interest for 4 years.
(2) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(4) In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?
(5) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7152 to clear the loan, then find the time period of the loan.
(6) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?
(7) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6664 to clear the loan, then find the time period of the loan.
(8) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.
(10) Sandra had to pay $4850.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.