Question:
Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
Correct Answer
$10300
Solution And Explanation
Solution
Given,
Principal (P) = $5150
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) = $5150 × 10% × 10
= $5150 ×10/100 × 10
= 5150 × 10 × 10/100
= 51500 × 10/100
= 515000/100
= $5150
Thus, Simple Interest = $5150
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 = $5150 + $5150
= $10300
Thus, Amount to be paid = $10300 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 = $5150
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 10 years
Thus, Amount (A)
= $5150 + ($5150 × 10% × 10)
= $5150 + ($5150 ×10/100 × 10)
= $5150 + (5150 × 10 × 10/100)
= $5150 + (51500 × 10/100)
= $5150 + (515000/100)
= $5150 + $5150 = $10300
Thus, Amount (A) to be paid = $10300 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 $5150, the simple interest in 1 year
= 10/100 × 5150
= 10 × 5150/100
= 51500/100 = $515
Thus, simple interest for 1 year = $515
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $515 × 10 = $5150
Thus, Simple Interest (SI) = $5150
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $5150
= $10300
Thus, Amount to be paid = $10300 Answer
Similar Questions
(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.
(2) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.
(3) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 4 years.
(5) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.
(6) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 3% simple interest?
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.
(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.
(9) Barbara had to pay $3976 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Margaret had to pay $4872 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.