Question:
Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.
Correct Answer
$9180
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 8%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $5100 × 8% × 10
= $5100 ×8/100 × 10
= 5100 × 8 × 10/100
= 40800 × 10/100
= 408000/100
= $4080
Thus, Simple Interest = $4080
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 = $5100 + $4080
= $9180
Thus, Amount to be paid = $9180 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 = $5100
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 10 years
Thus, Amount (A)
= $5100 + ($5100 × 8% × 10)
= $5100 + ($5100 ×8/100 × 10)
= $5100 + (5100 × 8 × 10/100)
= $5100 + (40800 × 10/100)
= $5100 + (408000/100)
= $5100 + $4080 = $9180
Thus, Amount (A) to be paid = $9180 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5100, the simple interest in 1 year
= 8/100 × 5100
= 8 × 5100/100
= 40800/100 = $408
Thus, simple interest for 1 year = $408
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $408 × 10 = $4080
Thus, Simple Interest (SI) = $4080
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $4080
= $9180
Thus, Amount to be paid = $9180 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(2) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(3) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(4) Charles had to pay $4368 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.
(6) Lisa had to pay $4657.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?
(8) How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?
(9) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.
(10) If Sandra paid $5340 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.