Question:
Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
Correct Answer
$9785
Solution And Explanation
Solution
Given,
Principal (P) = $5150
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) = $5150 × 10% × 9
= $5150 ×10/100 × 9
= 5150 × 10 × 9/100
= 51500 × 9/100
= 463500/100
= $4635
Thus, Simple Interest = $4635
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 + $4635
= $9785
Thus, Amount to be paid = $9785 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) = 9 years
Thus, Amount (A)
= $5150 + ($5150 × 10% × 9)
= $5150 + ($5150 ×10/100 × 9)
= $5150 + (5150 × 10 × 9/100)
= $5150 + (51500 × 9/100)
= $5150 + (463500/100)
= $5150 + $4635 = $9785
Thus, Amount (A) to be paid = $9785 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 9 years
= Simple interest for 1 year × 9
= $515 × 9 = $4635
Thus, Simple Interest (SI) = $4635
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $4635
= $9785
Thus, Amount to be paid = $9785 Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 4 years.
(2) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 5% simple interest?
(3) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 8 years.
(5) 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.
(6) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 8 years.
(7) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(8) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9248 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.
(10) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 2% simple interest.