Question:
Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.
Correct Answer
$7950
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 5%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 10
= $5300 ×5/100 × 10
= 5300 × 5 × 10/100
= 26500 × 10/100
= 265000/100
= $2650
Thus, Simple Interest = $2650
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 + $2650
= $7950
Thus, Amount to be paid = $7950 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) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5300 + ($5300 × 5% × 10)
= $5300 + ($5300 ×5/100 × 10)
= $5300 + (5300 × 5 × 10/100)
= $5300 + (26500 × 10/100)
= $5300 + (265000/100)
= $5300 + $2650 = $7950
Thus, Amount (A) to be paid = $7950 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5300, the simple interest in 1 year
= 5/100 × 5300
= 5 × 5300/100
= 26500/100 = $265
Thus, simple interest for 1 year = $265
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $265 × 10 = $2650
Thus, Simple Interest (SI) = $2650
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $2650
= $7950
Thus, Amount to be paid = $7950 Answer
Similar Questions
(1) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 4 years.
(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 8 years.
(3) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?
(4) How much loan did Matthew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7130 to clear it?
(5) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.
(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 4 years.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.
(10) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.