Question:
Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
Correct Answer
$10700
Solution And Explanation
Solution
Given,
Principal (P) = $5350
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) = $5350 × 10% × 10
= $5350 ×10/100 × 10
= 5350 × 10 × 10/100
= 53500 × 10/100
= 535000/100
= $5350
Thus, Simple Interest = $5350
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 = $5350 + $5350
= $10700
Thus, Amount to be paid = $10700 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 = $5350
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 10 years
Thus, Amount (A)
= $5350 + ($5350 × 10% × 10)
= $5350 + ($5350 ×10/100 × 10)
= $5350 + (5350 × 10 × 10/100)
= $5350 + (53500 × 10/100)
= $5350 + (535000/100)
= $5350 + $5350 = $10700
Thus, Amount (A) to be paid = $10700 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 $5350, the simple interest in 1 year
= 10/100 × 5350
= 10 × 5350/100
= 53500/100 = $535
Thus, simple interest for 1 year = $535
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $535 × 10 = $5350
Thus, Simple Interest (SI) = $5350
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $5350
= $10700
Thus, Amount to be paid = $10700 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.
(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 6% simple interest?
(3) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
(4) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9676 to clear the loan, then find the time period of the loan.
(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?
(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?
(8) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 7 years.
(10) 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.