Question:
Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.
Correct Answer
$6731
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 3%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 9
= $5300 ×3/100 × 9
= 5300 × 3 × 9/100
= 15900 × 9/100
= 143100/100
= $1431
Thus, Simple Interest = $1431
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 + $1431
= $6731
Thus, Amount to be paid = $6731 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) = 3%
And, Time (t) = 9 years
Thus, Amount (A)
= $5300 + ($5300 × 3% × 9)
= $5300 + ($5300 ×3/100 × 9)
= $5300 + (5300 × 3 × 9/100)
= $5300 + (15900 × 9/100)
= $5300 + (143100/100)
= $5300 + $1431 = $6731
Thus, Amount (A) to be paid = $6731 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5300, the simple interest in 1 year
= 3/100 × 5300
= 3 × 5300/100
= 15900/100 = $159
Thus, simple interest for 1 year = $159
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $159 × 9 = $1431
Thus, Simple Interest (SI) = $1431
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $1431
= $6731
Thus, Amount to be paid = $6731 Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(2) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 3 years.
(6) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(7) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.
(8) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?
(9) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.
(10) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.