Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 7 years.
Correct Answer
$6784
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 4%
Time (t) = 7 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% × 7
= $5300 ×4/100 × 7
= 5300 × 4 × 7/100
= 21200 × 7/100
= 148400/100
= $1484
Thus, Simple Interest = $1484
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 + $1484
= $6784
Thus, Amount to be paid = $6784 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) = 7 years
Thus, Amount (A)
= $5300 + ($5300 × 4% × 7)
= $5300 + ($5300 ×4/100 × 7)
= $5300 + (5300 × 4 × 7/100)
= $5300 + (21200 × 7/100)
= $5300 + (148400/100)
= $5300 + $1484 = $6784
Thus, Amount (A) to be paid = $6784 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 7 years
= Simple interest for 1 year × 7
= $212 × 7 = $1484
Thus, Simple Interest (SI) = $1484
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $1484
= $6784
Thus, Amount to be paid = $6784 Answer
Similar Questions
(1) How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?
(2) If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 3 years.
(5) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 5% simple interest?
(6) Mary had to pay $3233 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 3 years.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.
(9) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?
(10) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.