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) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?
(2) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
(3) How much loan did Susan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6215 to clear it?
(4) How much loan did Sandra borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7740 to clear it?
(5) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?
(7) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?
(8) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?
(9) If John borrowed $3200 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.