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) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?
(2) If Kenneth paid $5800 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.
(4) If John paid $3712 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?
(6) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?
(8) How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?
(9) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.
(10) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.