Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.
Correct Answer
$10030
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 10%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 7
= $5900 ×10/100 × 7
= 5900 × 10 × 7/100
= 59000 × 7/100
= 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) = 10%
And, Time (t) = 7 years
Thus, Amount (A)
= $5900 + ($5900 × 10% × 7)
= $5900 + ($5900 ×10/100 × 7)
= $5900 + (5900 × 10 × 7/100)
= $5900 + (59000 × 7/100)
= $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 = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5900, the simple interest in 1 year
= 10/100 × 5900
= 10 × 5900/100
= 59000/100 = $590
Thus, simple interest for 1 year = $590
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $590 × 7 = $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) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.
(3) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 4 years.
(5) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(6) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.
(7) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Christopher had to pay $4240 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 8 years.
(10) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.