Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.
Correct Answer
$9116
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 9%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 8
= $5300 ×9/100 × 8
= 5300 × 9 × 8/100
= 47700 × 8/100
= 381600/100
= $3816
Thus, Simple Interest = $3816
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 + $3816
= $9116
Thus, Amount to be paid = $9116 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) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5300 + ($5300 × 9% × 8)
= $5300 + ($5300 ×9/100 × 8)
= $5300 + (5300 × 9 × 8/100)
= $5300 + (47700 × 8/100)
= $5300 + (381600/100)
= $5300 + $3816 = $9116
Thus, Amount (A) to be paid = $9116 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5300, the simple interest in 1 year
= 9/100 × 5300
= 9 × 5300/100
= 47700/100 = $477
Thus, simple interest for 1 year = $477
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $477 × 8 = $3816
Thus, Simple Interest (SI) = $3816
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $3816
= $9116
Thus, Amount to be paid = $9116 Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 4 years.
(3) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.
(4) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.
(5) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.
(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.
(7) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(8) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
(10) What amount does John have to pay after 5 years if he takes a loan of $3200 at 10% simple interest?