Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 7 years.
Correct Answer
$7897
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 7%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 7
= $5300 ×7/100 × 7
= 5300 × 7 × 7/100
= 37100 × 7/100
= 259700/100
= $2597
Thus, Simple Interest = $2597
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 + $2597
= $7897
Thus, Amount to be paid = $7897 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) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5300 + ($5300 × 7% × 7)
= $5300 + ($5300 ×7/100 × 7)
= $5300 + (5300 × 7 × 7/100)
= $5300 + (37100 × 7/100)
= $5300 + (259700/100)
= $5300 + $2597 = $7897
Thus, Amount (A) to be paid = $7897 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5300, the simple interest in 1 year
= 7/100 × 5300
= 7 × 5300/100
= 37100/100 = $371
Thus, simple interest for 1 year = $371
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $371 × 7 = $2597
Thus, Simple Interest (SI) = $2597
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $2597
= $7897
Thus, Amount to be paid = $7897 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.
(2) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.
(3) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?
(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.
(5) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $12400 to clear the loan, then find the time period of the loan.
(6) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(7) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(8) How much loan did Ronald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8250 to clear it?
(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 8 years.
(10) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 7% simple interest?