Question:
Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.
Correct Answer
$7420
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 4%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 10
= $5300 ×4/100 × 10
= 5300 × 4 × 10/100
= 21200 × 10/100
= 212000/100
= $2120
Thus, Simple Interest = $2120
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 + $2120
= $7420
Thus, Amount to be paid = $7420 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) = 4%
And, Time (t) = 10 years
Thus, Amount (A)
= $5300 + ($5300 × 4% × 10)
= $5300 + ($5300 ×4/100 × 10)
= $5300 + (5300 × 4 × 10/100)
= $5300 + (21200 × 10/100)
= $5300 + (212000/100)
= $5300 + $2120 = $7420
Thus, Amount (A) to be paid = $7420 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5300, the simple interest in 1 year
= 4/100 × 5300
= 4 × 5300/100
= 21200/100 = $212
Thus, simple interest for 1 year = $212
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $212 × 10 = $2120
Thus, Simple Interest (SI) = $2120
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $2120
= $7420
Thus, Amount to be paid = $7420 Answer
Similar Questions
(1) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?
(2) Michael had to pay $3795 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?
(4) What amount does John have to pay after 5 years if he takes a loan of $3200 at 7% simple interest?
(5) How much loan did Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?
(6) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
(7) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?
(8) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?
(10) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 10% simple interest?