Question:
Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
Correct Answer
$9595
Solution And Explanation
Solution
Given,
Principal (P) = $5050
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) = $5050 × 10% × 9
= $5050 ×10/100 × 9
= 5050 × 10 × 9/100
= 50500 × 9/100
= 454500/100
= $4545
Thus, Simple Interest = $4545
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 = $5050 + $4545
= $9595
Thus, Amount to be paid = $9595 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 = $5050
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5050 + ($5050 × 10% × 9)
= $5050 + ($5050 ×10/100 × 9)
= $5050 + (5050 × 10 × 9/100)
= $5050 + (50500 × 9/100)
= $5050 + (454500/100)
= $5050 + $4545 = $9595
Thus, Amount (A) to be paid = $9595 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 $5050, the simple interest in 1 year
= 10/100 × 5050
= 10 × 5050/100
= 50500/100 = $505
Thus, simple interest for 1 year = $505
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $505 × 9 = $4545
Thus, Simple Interest (SI) = $4545
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $4545
= $9595
Thus, Amount to be paid = $9595 Answer
Similar Questions
(1) How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?
(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.
(3) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.
(5) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.
(6) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?
(7) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.
(8) If Nancy paid $4814 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 3 years.