Question:
Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.
Correct Answer
$6360
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 2%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 10
= $5300 ×2/100 × 10
= 5300 × 2 × 10/100
= 10600 × 10/100
= 106000/100
= $1060
Thus, Simple Interest = $1060
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 + $1060
= $6360
Thus, Amount to be paid = $6360 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) = 2%
And, Time (t) = 10 years
Thus, Amount (A)
= $5300 + ($5300 × 2% × 10)
= $5300 + ($5300 ×2/100 × 10)
= $5300 + (5300 × 2 × 10/100)
= $5300 + (10600 × 10/100)
= $5300 + (106000/100)
= $5300 + $1060 = $6360
Thus, Amount (A) to be paid = $6360 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5300, the simple interest in 1 year
= 2/100 × 5300
= 2 × 5300/100
= 10600/100 = $106
Thus, simple interest for 1 year = $106
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $106 × 10 = $1060
Thus, Simple Interest (SI) = $1060
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $1060
= $6360
Thus, Amount to be paid = $6360 Answer
Similar Questions
(1) How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?
(2) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.
(3) How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?
(4) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(5) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?
(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 8 years.
(8) John had to pay $3392 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.
(10) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.