Question:
Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 8 years.
Correct Answer
$6882
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5550 ×3/100 × 8
= 5550 × 3 × 8/100
= 16650 × 8/100
= 133200/100
= $1332
Thus, Simple Interest = $1332
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 + $1332
= $6882
Thus, Amount to be paid = $6882 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5550 + ($5550 × 3% × 8)
= $5550 + ($5550 ×3/100 × 8)
= $5550 + (5550 × 3 × 8/100)
= $5550 + (16650 × 8/100)
= $5550 + (133200/100)
= $5550 + $1332 = $6882
Thus, Amount (A) to be paid = $6882 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5550, the simple interest in 1 year
= 3/100 × 5550
= 3 × 5550/100
= 16650/100 = $166.5
Thus, simple interest for 1 year = $166.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $166.5 × 8 = $1332
Thus, Simple Interest (SI) = $1332
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $1332
= $6882
Thus, Amount to be paid = $6882 Answer
Similar Questions
(1) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 10% simple interest?
(2) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.
(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 3% simple interest?
(4) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8432 to clear the loan, then find the time period of the loan.
(5) If Anthony paid $4988 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?
(7) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(8) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?
(9) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.
(10) If Margaret paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.