Question:
Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 7 years.
Correct Answer
$7971.5
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 7%
Time (t) = 7 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) = $5350 × 7% × 7
= $5350 ×7/100 × 7
= 5350 × 7 × 7/100
= 37450 × 7/100
= 262150/100
= $2621.5
Thus, Simple Interest = $2621.5
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 = $5350 + $2621.5
= $7971.5
Thus, Amount to be paid = $7971.5 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 = $5350
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5350 + ($5350 × 7% × 7)
= $5350 + ($5350 ×7/100 × 7)
= $5350 + (5350 × 7 × 7/100)
= $5350 + (37450 × 7/100)
= $5350 + (262150/100)
= $5350 + $2621.5 = $7971.5
Thus, Amount (A) to be paid = $7971.5 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 $5350, the simple interest in 1 year
= 7/100 × 5350
= 7 × 5350/100
= 37450/100 = $374.5
Thus, simple interest for 1 year = $374.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $374.5 × 7 = $2621.5
Thus, Simple Interest (SI) = $2621.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $2621.5
= $7971.5
Thus, Amount to be paid = $7971.5 Answer
Similar Questions
(1) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11403 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(4) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?
(5) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 3% simple interest.
(6) Andrew had to pay $5520 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6540 to clear it?
(8) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 7% simple interest?
(9) How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?
(10) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?