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) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 5% per annum?
(2) If Donald paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.
(4) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?
(5) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 4 years.
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 7 years.
(7) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(8) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(9) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 8 years.
(10) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.