Question:
Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.
Correct Answer
$9116
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 8%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 9
= $5300 ×8/100 × 9
= 5300 × 8 × 9/100
= 42400 × 9/100
= 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) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5300 + ($5300 × 8% × 9)
= $5300 + ($5300 ×8/100 × 9)
= $5300 + (5300 × 8 × 9/100)
= $5300 + (42400 × 9/100)
= $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 = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5300, the simple interest in 1 year
= 8/100 × 5300
= 8 × 5300/100
= 42400/100 = $424
Thus, simple interest for 1 year = $424
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $424 × 9 = $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) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(2) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.
(3) If Joshua paid $5488 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?
(6) How much loan did Edward borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9500 to clear it?
(7) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.
(8) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 5% simple interest?
(9) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?
(10) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6724 to clear the loan, then find the time period of the loan.