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) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 6% simple interest?
(2) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 4 years.
(3) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?
(4) How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?
(5) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $8400 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?
(7) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?
(8) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.
(9) How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?
(10) If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.