Question:
Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.
Correct Answer
$9990
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 8
= $5550 ×10/100 × 8
= 5550 × 10 × 8/100
= 55500 × 8/100
= 444000/100
= $4440
Thus, Simple Interest = $4440
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 + $4440
= $9990
Thus, Amount to be paid = $9990 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5550 + ($5550 × 10% × 8)
= $5550 + ($5550 ×10/100 × 8)
= $5550 + (5550 × 10 × 8/100)
= $5550 + (55500 × 8/100)
= $5550 + (444000/100)
= $5550 + $4440 = $9990
Thus, Amount (A) to be paid = $9990 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5550, the simple interest in 1 year
= 10/100 × 5550
= 10 × 5550/100
= 55500/100 = $555
Thus, simple interest for 1 year = $555
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $555 × 8 = $4440
Thus, Simple Interest (SI) = $4440
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $4440
= $9990
Thus, Amount to be paid = $9990 Answer
Similar Questions
(1) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 4 years.
(2) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 3% simple interest.
(3) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 4 years.
(4) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $12200 to clear the loan, then find the time period of the loan.
(5) Joseph had to pay $4033 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 7 years.
(7) If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 4 years.
(10) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.