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) Kenneth had to pay $5300 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 4% simple interest?
(3) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(4) If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(5) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.
(6) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?
(7) 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.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 8 years.
(9) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(10) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 9% simple interest?