Question:
What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 3% simple interest?
Correct Answer
$4720
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (SI) = 3%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 6
= $4000 ×3/100 × 6
= 4000 × 3 × 6/100
= 12000 × 6/100
= 72000/100
= $720
Thus, Simple Interest = $720
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 + $720
= $4720
Thus, Amount to be paid = $4720 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) = 3%
And, Time (t) = 6 years
Thus, Amount (A)
= $4000 + ($4000 × 3% × 6)
= $4000 + ($4000 ×3/100 × 6)
= $4000 + (4000 × 3 × 6/100)
= $4000 + (12000 × 6/100)
= $4000 + (72000/100)
= $4000 + $720 = $4720
Thus, Amount (A) to be paid = $4720 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $4000, the simple interest in 1 year
= 3/100 × 4000
= 3 × 4000/100
= 12000/100 = $120
Thus, simple interest for 1 year = $120
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $120 × 6 = $720
Thus, Simple Interest (SI) = $720
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $4000 + $720
= $4720
Thus, Amount to be paid = $4720 Answer
Similar Questions
(1) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 3 years.
(2) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(3) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.
(5) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.
(7) How much loan did Barbara borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6382.5 to clear it?
(8) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(9) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 8 years.