Question:
Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
Correct Answer
$8025
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 5%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 10
= $5350 ×5/100 × 10
= 5350 × 5 × 10/100
= 26750 × 10/100
= 267500/100
= $2675
Thus, Simple Interest = $2675
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 + $2675
= $8025
Thus, Amount to be paid = $8025 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) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5350 + ($5350 × 5% × 10)
= $5350 + ($5350 ×5/100 × 10)
= $5350 + (5350 × 5 × 10/100)
= $5350 + (26750 × 10/100)
= $5350 + (267500/100)
= $5350 + $2675 = $8025
Thus, Amount (A) to be paid = $8025 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5350, the simple interest in 1 year
= 5/100 × 5350
= 5 × 5350/100
= 26750/100 = $267.5
Thus, simple interest for 1 year = $267.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $267.5 × 10 = $2675
Thus, Simple Interest (SI) = $2675
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $2675
= $8025
Thus, Amount to be paid = $8025 Answer
Similar Questions
(1) If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(3) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(4) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.
(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 2% simple interest?
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.
(8) William had to pay $4025 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 5% simple interest?
(10) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.