Question:
Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
Correct Answer
$10030
Solution And Explanation
Solution
Given,
Principal (P) = $5900
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) = $5900 × 7% × 10
= $5900 ×7/100 × 10
= 5900 × 7 × 10/100
= 41300 × 10/100
= 413000/100
= $4130
Thus, Simple Interest = $4130
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 = $5900 + $4130
= $10030
Thus, Amount to be paid = $10030 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 = $5900
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 10 years
Thus, Amount (A)
= $5900 + ($5900 × 7% × 10)
= $5900 + ($5900 ×7/100 × 10)
= $5900 + (5900 × 7 × 10/100)
= $5900 + (41300 × 10/100)
= $5900 + (413000/100)
= $5900 + $4130 = $10030
Thus, Amount (A) to be paid = $10030 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 $5900, the simple interest in 1 year
= 7/100 × 5900
= 7 × 5900/100
= 41300/100 = $413
Thus, simple interest for 1 year = $413
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $413 × 10 = $4130
Thus, Simple Interest (SI) = $4130
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $4130
= $10030
Thus, Amount to be paid = $10030 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.
(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 8 years.
(3) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.
(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 4 years.
(5) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?
(6) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(7) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 8 years.
(9) Daniel had to pay $4469 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.