Question:
Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 8 years.
Correct Answer
$7440
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 3%
Time (t) = 8 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) = $6000 × 3% × 8
= $6000 ×3/100 × 8
= 6000 × 3 × 8/100
= 18000 × 8/100
= 144000/100
= $1440
Thus, Simple Interest = $1440
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 = $6000 + $1440
= $7440
Thus, Amount to be paid = $7440 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 = $6000
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $6000 + ($6000 × 3% × 8)
= $6000 + ($6000 ×3/100 × 8)
= $6000 + (6000 × 3 × 8/100)
= $6000 + (18000 × 8/100)
= $6000 + (144000/100)
= $6000 + $1440 = $7440
Thus, Amount (A) to be paid = $7440 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 $6000, the simple interest in 1 year
= 3/100 × 6000
= 3 × 6000/100
= 18000/100 = $180
Thus, simple interest for 1 year = $180
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $180 × 8 = $1440
Thus, Simple Interest (SI) = $1440
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $1440
= $7440
Thus, Amount to be paid = $7440 Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 8 years.
(3) What amount will be due after 2 years if James borrowed a sum of $3000 at a 6% simple interest?
(4) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 7% simple interest?
(5) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.
(6) Paul had to pay $5264 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8856 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.
(9) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 3 years.
(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 8 years.