Question:
Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.
Correct Answer
$10070
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 9%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 10
= $5300 ×9/100 × 10
= 5300 × 9 × 10/100
= 47700 × 10/100
= 477000/100
= $4770
Thus, Simple Interest = $4770
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 + $4770
= $10070
Thus, Amount to be paid = $10070 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) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5300 + ($5300 × 9% × 10)
= $5300 + ($5300 ×9/100 × 10)
= $5300 + (5300 × 9 × 10/100)
= $5300 + (47700 × 10/100)
= $5300 + (477000/100)
= $5300 + $4770 = $10070
Thus, Amount (A) to be paid = $10070 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5300, the simple interest in 1 year
= 9/100 × 5300
= 9 × 5300/100
= 47700/100 = $477
Thus, simple interest for 1 year = $477
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $477 × 10 = $4770
Thus, Simple Interest (SI) = $4770
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $4770
= $10070
Thus, Amount to be paid = $10070 Answer
Similar Questions
(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 3 years.
(2) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
(3) Joshua had to pay $5635 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
(5) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?
(6) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.
(7) How much loan did Lisa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6655 to clear it?
(8) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.
(9) What amount does David have to pay after 6 years if he takes a loan of $3400 at 10% simple interest?
(10) What amount does James have to pay after 6 years if he takes a loan of $3000 at 3% simple interest?