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) David had to pay $3808 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5712 to clear the loan, then find the time period of the loan.
(3) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 4 years.
(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 2% simple interest?
(6) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 3 years.
(8) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(10) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.