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) Margaret had to pay $4611 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.
(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 3% simple interest?
(5) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
(7) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 8 years.
(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 7 years.
(9) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
(10) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.