Question:
Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.
Correct Answer
$7420
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 4%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 10
= $5300 ×4/100 × 10
= 5300 × 4 × 10/100
= 21200 × 10/100
= 212000/100
= $2120
Thus, Simple Interest = $2120
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 + $2120
= $7420
Thus, Amount to be paid = $7420 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) = 4%
And, Time (t) = 10 years
Thus, Amount (A)
= $5300 + ($5300 × 4% × 10)
= $5300 + ($5300 ×4/100 × 10)
= $5300 + (5300 × 4 × 10/100)
= $5300 + (21200 × 10/100)
= $5300 + (212000/100)
= $5300 + $2120 = $7420
Thus, Amount (A) to be paid = $7420 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5300, the simple interest in 1 year
= 4/100 × 5300
= 4 × 5300/100
= 21200/100 = $212
Thus, simple interest for 1 year = $212
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $212 × 10 = $2120
Thus, Simple Interest (SI) = $2120
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $2120
= $7420
Thus, Amount to be paid = $7420 Answer
Similar Questions
(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.
(2) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7980 to clear it?
(3) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(4) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(5) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(6) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?
(7) If Nancy paid $4814 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.
(9) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.
(10) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?