Question:
Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 4 years.
Correct Answer
$4800
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (SI) = 5%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 4
= $4000 ×5/100 × 4
= 4000 × 5 × 4/100
= 20000 × 4/100
= 80000/100
= $800
Thus, Simple Interest = $800
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 + $800
= $4800
Thus, Amount to be paid = $4800 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) = 5%
And, Time (t) = 4 years
Thus, Amount (A)
= $4000 + ($4000 × 5% × 4)
= $4000 + ($4000 ×5/100 × 4)
= $4000 + (4000 × 5 × 4/100)
= $4000 + (20000 × 4/100)
= $4000 + (80000/100)
= $4000 + $800 = $4800
Thus, Amount (A) to be paid = $4800 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $4000, the simple interest in 1 year
= 5/100 × 4000
= 5 × 4000/100
= 20000/100 = $200
Thus, simple interest for 1 year = $200
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $200 × 4 = $800
Thus, Simple Interest (SI) = $800
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $4000 + $800
= $4800
Thus, Amount to be paid = $4800 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
(3) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(4) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?
(5) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?
(6) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.
(7) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.
(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?
(10) Paul had to pay $5405 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.