Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 8 years.
Correct Answer
$6324
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5100 ×3/100 × 8
= 5100 × 3 × 8/100
= 15300 × 8/100
= 122400/100
= $1224
Thus, Simple Interest = $1224
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 + $1224
= $6324
Thus, Amount to be paid = $6324 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5100 + ($5100 × 3% × 8)
= $5100 + ($5100 ×3/100 × 8)
= $5100 + (5100 × 3 × 8/100)
= $5100 + (15300 × 8/100)
= $5100 + (122400/100)
= $5100 + $1224 = $6324
Thus, Amount (A) to be paid = $6324 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5100, the simple interest in 1 year
= 3/100 × 5100
= 3 × 5100/100
= 15300/100 = $153
Thus, simple interest for 1 year = $153
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $153 × 8 = $1224
Thus, Simple Interest (SI) = $1224
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $1224
= $6324
Thus, Amount to be paid = $6324 Answer
Similar Questions
(1) 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.
(2) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.
(3) Daniel had to pay $4469 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) If Betty paid $4930 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 8 years.
(6) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.
(7) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.
(8) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
(9) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.
(10) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 4 years.