Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 8 years.
Correct Answer
$7316
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5900 ×3/100 × 8
= 5900 × 3 × 8/100
= 17700 × 8/100
= 141600/100
= $1416
Thus, Simple Interest = $1416
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 + $1416
= $7316
Thus, Amount to be paid = $7316 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5900 + ($5900 × 3% × 8)
= $5900 + ($5900 ×3/100 × 8)
= $5900 + (5900 × 3 × 8/100)
= $5900 + (17700 × 8/100)
= $5900 + (141600/100)
= $5900 + $1416 = $7316
Thus, Amount (A) to be paid = $7316 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5900, the simple interest in 1 year
= 3/100 × 5900
= 3 × 5900/100
= 17700/100 = $177
Thus, simple interest for 1 year = $177
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $177 × 8 = $1416
Thus, Simple Interest (SI) = $1416
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $1416
= $7316
Thus, Amount to be paid = $7316 Answer
Similar Questions
(1) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 7 years.
(4) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?
(5) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?
(6) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
(7) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6258 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.
(9) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.
(10) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.