Question:
What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 5% simple interest?
Correct Answer
$5000
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (SI) = 5%
Time (t) = 5 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% × 5
= $4000 ×5/100 × 5
= 4000 × 5 × 5/100
= 20000 × 5/100
= 100000/100
= $1000
Thus, Simple Interest = $1000
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 + $1000
= $5000
Thus, Amount to be paid = $5000 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) = 5 years
Thus, Amount (A)
= $4000 + ($4000 × 5% × 5)
= $4000 + ($4000 ×5/100 × 5)
= $4000 + (4000 × 5 × 5/100)
= $4000 + (20000 × 5/100)
= $4000 + (100000/100)
= $4000 + $1000 = $5000
Thus, Amount (A) to be paid = $5000 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 5 years
= Simple interest for 1 year × 5
= $200 × 5 = $1000
Thus, Simple Interest (SI) = $1000
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $4000 + $1000
= $5000
Thus, Amount to be paid = $5000 Answer
Similar Questions
(1) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?
(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 6% simple interest?
(3) If Richard borrowed $3600 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 8 years.
(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.
(6) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 4% simple interest?
(7) What amount does John have to pay after 5 years if he takes a loan of $3200 at 7% simple interest?
(8) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.
(9) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 5% simple interest?