Question:
Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.
Correct Answer
$10148
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 8%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 9
= $5900 ×8/100 × 9
= 5900 × 8 × 9/100
= 47200 × 9/100
= 424800/100
= $4248
Thus, Simple Interest = $4248
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 + $4248
= $10148
Thus, Amount to be paid = $10148 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) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5900 + ($5900 × 8% × 9)
= $5900 + ($5900 ×8/100 × 9)
= $5900 + (5900 × 8 × 9/100)
= $5900 + (47200 × 9/100)
= $5900 + (424800/100)
= $5900 + $4248 = $10148
Thus, Amount (A) to be paid = $10148 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5900, the simple interest in 1 year
= 8/100 × 5900
= 8 × 5900/100
= 47200/100 = $472
Thus, simple interest for 1 year = $472
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $472 × 9 = $4248
Thus, Simple Interest (SI) = $4248
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $4248
= $10148
Thus, Amount to be paid = $10148 Answer
Similar Questions
(1) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.
(3) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.
(4) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(6) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.
(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 7 years.
(8) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11316 to clear the loan, then find the time period of the loan.
(9) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 10% simple interest?
(10) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.