Question:
What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?
Correct Answer
$5400
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (SI) = 7%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $4000 × 7% × 5
= $4000 ×7/100 × 5
= 4000 × 7 × 5/100
= 28000 × 5/100
= 140000/100
= $1400
Thus, Simple Interest = $1400
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 = $4000 + $1400
= $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 = $4000
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 5 years
Thus, Amount (A)
= $4000 + ($4000 × 7% × 5)
= $4000 + ($4000 ×7/100 × 5)
= $4000 + (4000 × 7 × 5/100)
= $4000 + (28000 × 5/100)
= $4000 + (140000/100)
= $4000 + $1400 = $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 = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $4000, the simple interest in 1 year
= 7/100 × 4000
= 7 × 4000/100
= 28000/100 = $280
Thus, simple interest for 1 year = $280
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $280 × 5 = $1400
Thus, Simple Interest (SI) = $1400
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $4000 + $1400
= $5400
Thus, Amount to be paid = $5400 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.
(2) How much loan did Nancy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6765 to clear it?
(3) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.
(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.
(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 7 years.
(6) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?
(7) David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?
(9) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 8 years.