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) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $10000 to clear the loan, then find the time period of the loan.
(2) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.
(3) If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Joshua had to pay $5194 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.
(6) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?
(7) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 3% simple interest?
(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?
(9) How much loan did Ryan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9480 to clear it?
(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 4 years.