Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.
Correct Answer
$9180
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 10%
Time (t) = 8 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) = $5100 × 10% × 8
= $5100 ×10/100 × 8
= 5100 × 10 × 8/100
= 51000 × 8/100
= 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5100 + ($5100 × 10% × 8)
= $5100 + ($5100 ×10/100 × 8)
= $5100 + (5100 × 10 × 8/100)
= $5100 + (51000 × 8/100)
= $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 = 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 $5100, the simple interest in 1 year
= 10/100 × 5100
= 10 × 5100/100
= 51000/100 = $510
Thus, simple interest for 1 year = $510
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $510 × 8 = $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) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Steven had to pay $5290 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.
(5) Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 6% simple interest?
(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 8 years.
(9) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 4 years.
(10) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.