Question:
Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
Correct Answer
$8585
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 7%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 10
= $5050 ×7/100 × 10
= 5050 × 7 × 10/100
= 35350 × 10/100
= 353500/100
= $3535
Thus, Simple Interest = $3535
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 + $3535
= $8585
Thus, Amount to be paid = $8585 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) = 7%
And, Time (t) = 10 years
Thus, Amount (A)
= $5050 + ($5050 × 7% × 10)
= $5050 + ($5050 ×7/100 × 10)
= $5050 + (5050 × 7 × 10/100)
= $5050 + (35350 × 10/100)
= $5050 + (353500/100)
= $5050 + $3535 = $8585
Thus, Amount (A) to be paid = $8585 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5050, the simple interest in 1 year
= 7/100 × 5050
= 7 × 5050/100
= 35350/100 = $353.5
Thus, simple interest for 1 year = $353.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $353.5 × 10 = $3535
Thus, Simple Interest (SI) = $3535
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $3535
= $8585
Thus, Amount to be paid = $8585 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.
(2) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
(4) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.
(5) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(6) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(7) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(8) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.
(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.