Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 8 years.
Correct Answer
$6732
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 4%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 8
= $5100 ×4/100 × 8
= 5100 × 4 × 8/100
= 20400 × 8/100
= 163200/100
= $1632
Thus, Simple Interest = $1632
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 + $1632
= $6732
Thus, Amount to be paid = $6732 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) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5100 + ($5100 × 4% × 8)
= $5100 + ($5100 ×4/100 × 8)
= $5100 + (5100 × 4 × 8/100)
= $5100 + (20400 × 8/100)
= $5100 + (163200/100)
= $5100 + $1632 = $6732
Thus, Amount (A) to be paid = $6732 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5100, the simple interest in 1 year
= 4/100 × 5100
= 4 × 5100/100
= 20400/100 = $204
Thus, simple interest for 1 year = $204
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $204 × 8 = $1632
Thus, Simple Interest (SI) = $1632
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $1632
= $6732
Thus, Amount to be paid = $6732 Answer
Similar Questions
(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 8 years.
(2) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(3) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.
(4) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?
(5) Joshua had to pay $5635 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.
(7) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?
(9) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?
(10) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.