Question:
Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
Correct Answer
$11500
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 10%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 10
= $5750 ×10/100 × 10
= 5750 × 10 × 10/100
= 57500 × 10/100
= 575000/100
= $5750
Thus, Simple Interest = $5750
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 + $5750
= $11500
Thus, Amount to be paid = $11500 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) = 10%
And, Time (t) = 10 years
Thus, Amount (A)
= $5750 + ($5750 × 10% × 10)
= $5750 + ($5750 ×10/100 × 10)
= $5750 + (5750 × 10 × 10/100)
= $5750 + (57500 × 10/100)
= $5750 + (575000/100)
= $5750 + $5750 = $11500
Thus, Amount (A) to be paid = $11500 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5750, the simple interest in 1 year
= 10/100 × 5750
= 10 × 5750/100
= 57500/100 = $575
Thus, simple interest for 1 year = $575
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $575 × 10 = $5750
Thus, Simple Interest (SI) = $5750
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $5750
= $11500
Thus, Amount to be paid = $11500 Answer
Similar Questions
(1) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.
(2) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?
(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) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 8 years.
(5) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(6) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(8) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.
(10) What amount does John have to pay after 5 years if he takes a loan of $3200 at 10% simple interest?