Question:
Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.
Correct Answer
$9010
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 7%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 10
= $5300 ×7/100 × 10
= 5300 × 7 × 10/100
= 37100 × 10/100
= 371000/100
= $3710
Thus, Simple Interest = $3710
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 + $3710
= $9010
Thus, Amount to be paid = $9010 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) = 7%
And, Time (t) = 10 years
Thus, Amount (A)
= $5300 + ($5300 × 7% × 10)
= $5300 + ($5300 ×7/100 × 10)
= $5300 + (5300 × 7 × 10/100)
= $5300 + (37100 × 10/100)
= $5300 + (371000/100)
= $5300 + $3710 = $9010
Thus, Amount (A) to be paid = $9010 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5300, the simple interest in 1 year
= 7/100 × 5300
= 7 × 5300/100
= 37100/100 = $371
Thus, simple interest for 1 year = $371
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $371 × 10 = $3710
Thus, Simple Interest (SI) = $3710
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $3710
= $9010
Thus, Amount to be paid = $9010 Answer
Similar Questions
(1) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.
(3) Barbara had to pay $3763 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 7 years.
(5) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 3 years.
(6) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 4% simple interest?
(7) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.
(8) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.
(9) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 6% simple interest?