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 if Sarah borrowed a sum of $3850 at 7% simple interest for 4 years.
(2) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
(3) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(4) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 6% simple interest?
(5) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.
(7) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 4 years.
(8) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.
(9) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(10) Lisa had to pay $4657.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.