Question:
What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 8% simple interest?
Correct Answer
$5328
Solution And Explanation
Solution
Given,
Principal (P) = $3600
Rate of Simple Interest (SI) = 8%
Time (t) = 6 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) = $3600 × 8% × 6
= $3600 ×8/100 × 6
= 3600 × 8 × 6/100
= 28800 × 6/100
= 172800/100
= $1728
Thus, Simple Interest = $1728
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 = $3600 + $1728
= $5328
Thus, Amount to be paid = $5328 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 = $3600
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 6 years
Thus, Amount (A)
= $3600 + ($3600 × 8% × 6)
= $3600 + ($3600 ×8/100 × 6)
= $3600 + (3600 × 8 × 6/100)
= $3600 + (28800 × 6/100)
= $3600 + (172800/100)
= $3600 + $1728 = $5328
Thus, Amount (A) to be paid = $5328 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 $3600, the simple interest in 1 year
= 8/100 × 3600
= 8 × 3600/100
= 28800/100 = $288
Thus, simple interest for 1 year = $288
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $288 × 6 = $1728
Thus, Simple Interest (SI) = $1728
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3600 + $1728
= $5328
Thus, Amount to be paid = $5328 Answer
Similar Questions
(1) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(2) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.
(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 8 years.
(6) 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?
(7) Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) If Elizabeth paid $4002 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.
(10) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.