Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 8 years.
Correct Answer
$7844
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 8
= $5300 ×6/100 × 8
= 5300 × 6 × 8/100
= 31800 × 8/100
= 254400/100
= $2544
Thus, Simple Interest = $2544
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 + $2544
= $7844
Thus, Amount to be paid = $7844 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) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5300 + ($5300 × 6% × 8)
= $5300 + ($5300 ×6/100 × 8)
= $5300 + (5300 × 6 × 8/100)
= $5300 + (31800 × 8/100)
= $5300 + (254400/100)
= $5300 + $2544 = $7844
Thus, Amount (A) to be paid = $7844 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5300, the simple interest in 1 year
= 6/100 × 5300
= 6 × 5300/100
= 31800/100 = $318
Thus, simple interest for 1 year = $318
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $318 × 8 = $2544
Thus, Simple Interest (SI) = $2544
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $2544
= $7844
Thus, Amount to be paid = $7844 Answer
Similar Questions
(1) How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?
(2) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 7% simple interest?
(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.
(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?
(5) How much loan did Brian borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7920 to clear it?
(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 4 years.
(7) If Daniel paid $4592 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
(9) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 7 years.