Question:
Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
Correct Answer
$6372
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 2%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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) = $5400 × 2% × 9
= $5400 ×2/100 × 9
= 5400 × 2 × 9/100
= 10800 × 9/100
= 97200/100
= $972
Thus, Simple Interest = $972
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 = $5400 + $972
= $6372
Thus, Amount to be paid = $6372 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 = $5400
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 9 years
Thus, Amount (A)
= $5400 + ($5400 × 2% × 9)
= $5400 + ($5400 ×2/100 × 9)
= $5400 + (5400 × 2 × 9/100)
= $5400 + (10800 × 9/100)
= $5400 + (97200/100)
= $5400 + $972 = $6372
Thus, Amount (A) to be paid = $6372 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5400, the simple interest in 1 year
= 2/100 × 5400
= 2 × 5400/100
= 10800/100 = $108
Thus, simple interest for 1 year = $108
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $108 × 9 = $972
Thus, Simple Interest (SI) = $972
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $972
= $6372
Thus, Amount to be paid = $6372 Answer
Similar Questions
(1) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
(3) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 7 years.
(5) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.
(7) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(8) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.
(9) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 10% simple interest?