Question:
Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.
Correct Answer
$10925
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 9%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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) = $5750 × 9% × 10
= $5750 ×9/100 × 10
= 5750 × 9 × 10/100
= 51750 × 10/100
= 517500/100
= $5175
Thus, Simple Interest = $5175
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 = $5750 + $5175
= $10925
Thus, Amount to be paid = $10925 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 = $5750
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5750 + ($5750 × 9% × 10)
= $5750 + ($5750 ×9/100 × 10)
= $5750 + (5750 × 9 × 10/100)
= $5750 + (51750 × 10/100)
= $5750 + (517500/100)
= $5750 + $5175 = $10925
Thus, Amount (A) to be paid = $10925 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5750, the simple interest in 1 year
= 9/100 × 5750
= 9 × 5750/100
= 51750/100 = $517.5
Thus, simple interest for 1 year = $517.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $517.5 × 10 = $5175
Thus, Simple Interest (SI) = $5175
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $5175
= $10925
Thus, Amount to be paid = $10925 Answer
Similar Questions
(1) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(2) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 7 years.
(4) What amount does John have to pay after 6 years if he takes a loan of $3200 at 6% simple interest?
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 7 years.
(6) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
(7) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?
(8) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?
(9) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(10) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.