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) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(2) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.
(4) Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 8 years.
(8) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(9) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?
(10) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.