Question:
Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.
Correct Answer
$6890
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 3%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 10
= $5300 ×3/100 × 10
= 5300 × 3 × 10/100
= 15900 × 10/100
= 159000/100
= $1590
Thus, Simple Interest = $1590
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 + $1590
= $6890
Thus, Amount to be paid = $6890 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) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5300 + ($5300 × 3% × 10)
= $5300 + ($5300 ×3/100 × 10)
= $5300 + (5300 × 3 × 10/100)
= $5300 + (15900 × 10/100)
= $5300 + (159000/100)
= $5300 + $1590 = $6890
Thus, Amount (A) to be paid = $6890 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5300, the simple interest in 1 year
= 3/100 × 5300
= 3 × 5300/100
= 15900/100 = $159
Thus, simple interest for 1 year = $159
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $159 × 10 = $1590
Thus, Simple Interest (SI) = $1590
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $1590
= $6890
Thus, Amount to be paid = $6890 Answer
Similar Questions
(1) How much loan did Daniel borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7015 to clear it?
(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 4% simple interest?
(3) In how much time a principal of $3000 will amount to $3600 at a simple interest of 4% per annum?
(4) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 7 years.
(6) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.
(7) If Mark paid $5104 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Kimberly had to pay $5068.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) If Elizabeth paid $3726 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.