Question:
What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 10% simple interest?
Correct Answer
$5400
Solution And Explanation
Solution
Given,
Principal (P) = $3600
Rate of Simple Interest (SI) = 10%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 5
= $3600 ×10/100 × 5
= 3600 × 10 × 5/100
= 36000 × 5/100
= 180000/100
= $1800
Thus, Simple Interest = $1800
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 + $1800
= $5400
Thus, Amount to be paid = $5400 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) = 10%
And, Time (t) = 5 years
Thus, Amount (A)
= $3600 + ($3600 × 10% × 5)
= $3600 + ($3600 ×10/100 × 5)
= $3600 + (3600 × 10 × 5/100)
= $3600 + (36000 × 5/100)
= $3600 + (180000/100)
= $3600 + $1800 = $5400
Thus, Amount (A) to be paid = $5400 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3600, the simple interest in 1 year
= 10/100 × 3600
= 10 × 3600/100
= 36000/100 = $360
Thus, simple interest for 1 year = $360
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $360 × 5 = $1800
Thus, Simple Interest (SI) = $1800
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3600 + $1800
= $5400
Thus, Amount to be paid = $5400 Answer
Similar Questions
(1) Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 5% simple interest.
(3) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.
(4) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan.
(5) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?
(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.
(7) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?
(8) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(9) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?
(10) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.