Question:
Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 7 years.
Correct Answer
$7492.5
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 5%
Time (t) = 7 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) = $5550 × 5% × 7
= $5550 ×5/100 × 7
= 5550 × 5 × 7/100
= 27750 × 7/100
= 194250/100
= $1942.5
Thus, Simple Interest = $1942.5
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 = $5550 + $1942.5
= $7492.5
Thus, Amount to be paid = $7492.5 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 = $5550
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5550 + ($5550 × 5% × 7)
= $5550 + ($5550 ×5/100 × 7)
= $5550 + (5550 × 5 × 7/100)
= $5550 + (27750 × 7/100)
= $5550 + (194250/100)
= $5550 + $1942.5 = $7492.5
Thus, Amount (A) to be paid = $7492.5 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 $5550, the simple interest in 1 year
= 5/100 × 5550
= 5 × 5550/100
= 27750/100 = $277.5
Thus, simple interest for 1 year = $277.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $277.5 × 7 = $1942.5
Thus, Simple Interest (SI) = $1942.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $1942.5
= $7492.5
Thus, Amount to be paid = $7492.5 Answer
Similar Questions
(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 3 years.
(2) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9238 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 4 years.
(4) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.
(5) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?
(6) If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(8) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 5% simple interest?
(9) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.