Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 7 years.
Correct Answer
$5757
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 2%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 7
= $5050 ×2/100 × 7
= 5050 × 2 × 7/100
= 10100 × 7/100
= 70700/100
= $707
Thus, Simple Interest = $707
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 + $707
= $5757
Thus, Amount to be paid = $5757 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) = 2%
And, Time (t) = 7 years
Thus, Amount (A)
= $5050 + ($5050 × 2% × 7)
= $5050 + ($5050 ×2/100 × 7)
= $5050 + (5050 × 2 × 7/100)
= $5050 + (10100 × 7/100)
= $5050 + (70700/100)
= $5050 + $707 = $5757
Thus, Amount (A) to be paid = $5757 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5050, the simple interest in 1 year
= 2/100 × 5050
= 2 × 5050/100
= 10100/100 = $101
Thus, simple interest for 1 year = $101
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $101 × 7 = $707
Thus, Simple Interest (SI) = $707
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $707
= $5757
Thus, Amount to be paid = $5757 Answer
Similar Questions
(1) If Patricia paid $3528 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?
(3) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.
(4) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 4 years.
(5) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.
(7) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(8) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
(10) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.