Question:
Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
Correct Answer
$9595
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 9%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 10
= $5050 ×9/100 × 10
= 5050 × 9 × 10/100
= 45450 × 10/100
= 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) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5050 + ($5050 × 9% × 10)
= $5050 + ($5050 ×9/100 × 10)
= $5050 + (5050 × 9 × 10/100)
= $5050 + (45450 × 10/100)
= $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 = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5050, the simple interest in 1 year
= 9/100 × 5050
= 9 × 5050/100
= 45450/100 = $454.5
Thus, simple interest for 1 year = $454.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $454.5 × 10 = $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) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.
(2) What amount will be due after 2 years if David borrowed a sum of $3200 at a 7% simple interest?
(3) 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.
(4) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(5) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?
(6) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.
(7) If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) If Linda paid $4020 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?
(10) If David borrowed $3400 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.