Question:
What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 6% simple interest?
Correct Answer
$5200
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (SI) = 6%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 5
= $4000 ×6/100 × 5
= 4000 × 6 × 5/100
= 24000 × 5/100
= 120000/100
= $1200
Thus, Simple Interest = $1200
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 + $1200
= $5200
Thus, Amount to be paid = $5200 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) = 6%
And, Time (t) = 5 years
Thus, Amount (A)
= $4000 + ($4000 × 6% × 5)
= $4000 + ($4000 ×6/100 × 5)
= $4000 + (4000 × 6 × 5/100)
= $4000 + (24000 × 5/100)
= $4000 + (120000/100)
= $4000 + $1200 = $5200
Thus, Amount (A) to be paid = $5200 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $4000, the simple interest in 1 year
= 6/100 × 4000
= 6 × 4000/100
= 24000/100 = $240
Thus, simple interest for 1 year = $240
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $240 × 5 = $1200
Thus, Simple Interest (SI) = $1200
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $4000 + $1200
= $5200
Thus, Amount to be paid = $5200 Answer
Similar Questions
(1) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.
(2) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8312.5 to clear it?
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 3 years.
(4) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(6) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7616 to clear the loan, then find the time period of the loan.
(7) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
(8) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(9) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 4 years.