Question:
What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?
Correct Answer
$4340
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 8%
Time (t) = 5 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) = $3100 × 8% × 5
= $3100 ×8/100 × 5
= 3100 × 8 × 5/100
= 24800 × 5/100
= 124000/100
= $1240
Thus, Simple Interest = $1240
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 = $3100 + $1240
= $4340
Thus, Amount to be paid = $4340 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 = $3100
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 5 years
Thus, Amount (A)
= $3100 + ($3100 × 8% × 5)
= $3100 + ($3100 ×8/100 × 5)
= $3100 + (3100 × 8 × 5/100)
= $3100 + (24800 × 5/100)
= $3100 + (124000/100)
= $3100 + $1240 = $4340
Thus, Amount (A) to be paid = $4340 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 $3100, the simple interest in 1 year
= 8/100 × 3100
= 8 × 3100/100
= 24800/100 = $248
Thus, simple interest for 1 year = $248
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $248 × 5 = $1240
Thus, Simple Interest (SI) = $1240
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $1240
= $4340
Thus, Amount to be paid = $4340 Answer
Similar Questions
(1) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?
(2) If Jessica paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 9% simple interest?
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 7 years.
(5) How much loan did Mary borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6312.5 to clear it?
(6) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.
(9) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.
(10) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.