Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 7 years.
Correct Answer
$7965
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 5%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 7
= $5900 ×5/100 × 7
= 5900 × 5 × 7/100
= 29500 × 7/100
= 206500/100
= $2065
Thus, Simple Interest = $2065
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 + $2065
= $7965
Thus, Amount to be paid = $7965 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) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5900 + ($5900 × 5% × 7)
= $5900 + ($5900 ×5/100 × 7)
= $5900 + (5900 × 5 × 7/100)
= $5900 + (29500 × 7/100)
= $5900 + (206500/100)
= $5900 + $2065 = $7965
Thus, Amount (A) to be paid = $7965 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5900, the simple interest in 1 year
= 5/100 × 5900
= 5 × 5900/100
= 29500/100 = $295
Thus, simple interest for 1 year = $295
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $295 × 7 = $2065
Thus, Simple Interest (SI) = $2065
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $2065
= $7965
Thus, Amount to be paid = $7965 Answer
Similar Questions
(1) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 3 years.
(3) In how much time a principal of $3150 will amount to $3339 at a simple interest of 3% per annum?
(4) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?
(5) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) How much loan did Emily borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8100 to clear it?
(7) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.
(8) If Karen borrowed $3950 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 8 years.
(10) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 8 years.