Question:
Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.
Correct Answer
$8160
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 4%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 9
= $6000 ×4/100 × 9
= 6000 × 4 × 9/100
= 24000 × 9/100
= 216000/100
= $2160
Thus, Simple Interest = $2160
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 + $2160
= $8160
Thus, Amount to be paid = $8160 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) = 4%
And, Time (t) = 9 years
Thus, Amount (A)
= $6000 + ($6000 × 4% × 9)
= $6000 + ($6000 ×4/100 × 9)
= $6000 + (6000 × 4 × 9/100)
= $6000 + (24000 × 9/100)
= $6000 + (216000/100)
= $6000 + $2160 = $8160
Thus, Amount (A) to be paid = $8160 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $6000, the simple interest in 1 year
= 4/100 × 6000
= 4 × 6000/100
= 24000/100 = $240
Thus, simple interest for 1 year = $240
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $240 × 9 = $2160
Thus, Simple Interest (SI) = $2160
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $2160
= $8160
Thus, Amount to be paid = $8160 Answer
Similar Questions
(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 4 years.
(2) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 3% simple interest?
(3) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.
(4) What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?
(5) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 6% simple interest?
(7) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?
(8) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
(9) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?