Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 8 years.
Correct Answer
$8268
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 7%
Time (t) = 8 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% × 8
= $5300 ×7/100 × 8
= 5300 × 7 × 8/100
= 37100 × 8/100
= 296800/100
= $2968
Thus, Simple Interest = $2968
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 + $2968
= $8268
Thus, Amount to be paid = $8268 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) = 8 years
Thus, Amount (A)
= $5300 + ($5300 × 7% × 8)
= $5300 + ($5300 ×7/100 × 8)
= $5300 + (5300 × 7 × 8/100)
= $5300 + (37100 × 8/100)
= $5300 + (296800/100)
= $5300 + $2968 = $8268
Thus, Amount (A) to be paid = $8268 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 8 years
= Simple interest for 1 year × 8
= $371 × 8 = $2968
Thus, Simple Interest (SI) = $2968
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $2968
= $8268
Thus, Amount to be paid = $8268 Answer
Similar Questions
(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 3 years.
(2) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
(3) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(4) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(6) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 3 years.
(8) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?
(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 7 years.