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) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
(2) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.
(3) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.
(6) 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.
(7) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12127 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.
(9) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.