Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 8 years.
Correct Answer
$7788
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 4%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 8
= $5900 ×4/100 × 8
= 5900 × 4 × 8/100
= 23600 × 8/100
= 188800/100
= $1888
Thus, Simple Interest = $1888
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 + $1888
= $7788
Thus, Amount to be paid = $7788 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) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5900 + ($5900 × 4% × 8)
= $5900 + ($5900 ×4/100 × 8)
= $5900 + (5900 × 4 × 8/100)
= $5900 + (23600 × 8/100)
= $5900 + (188800/100)
= $5900 + $1888 = $7788
Thus, Amount (A) to be paid = $7788 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5900, the simple interest in 1 year
= 4/100 × 5900
= 4 × 5900/100
= 23600/100 = $236
Thus, simple interest for 1 year = $236
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $236 × 8 = $1888
Thus, Simple Interest (SI) = $1888
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $1888
= $7788
Thus, Amount to be paid = $7788 Answer
Similar Questions
(1) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 3 years.
(4) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.
(5) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(6) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(8) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?
(9) If Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?