Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.
Correct Answer
$6042
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 2%
Time (t) = 7 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) = $5300 × 2% × 7
= $5300 ×2/100 × 7
= 5300 × 2 × 7/100
= 10600 × 7/100
= 74200/100
= $742
Thus, Simple Interest = $742
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 = $5300 + $742
= $6042
Thus, Amount to be paid = $6042 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 = $5300
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 7 years
Thus, Amount (A)
= $5300 + ($5300 × 2% × 7)
= $5300 + ($5300 ×2/100 × 7)
= $5300 + (5300 × 2 × 7/100)
= $5300 + (10600 × 7/100)
= $5300 + (74200/100)
= $5300 + $742 = $6042
Thus, Amount (A) to be paid = $6042 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 $5300, the simple interest in 1 year
= 2/100 × 5300
= 2 × 5300/100
= 10600/100 = $106
Thus, simple interest for 1 year = $106
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $106 × 7 = $742
Thus, Simple Interest (SI) = $742
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $742
= $6042
Thus, Amount to be paid = $6042 Answer
Similar Questions
(1) 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.
(2) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 4% simple interest?
(4) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?
(5) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?
(7) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 6% simple interest?
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 3 years.
(9) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 4 years.
(10) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.