Question:
Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.
Correct Answer
$8658
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 7%
Time (t) = 8 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) = $5550 × 7% × 8
= $5550 ×7/100 × 8
= 5550 × 7 × 8/100
= 38850 × 8/100
= 310800/100
= $3108
Thus, Simple Interest = $3108
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 + $3108
= $8658
Thus, Amount to be paid = $8658 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) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5550 + ($5550 × 7% × 8)
= $5550 + ($5550 ×7/100 × 8)
= $5550 + (5550 × 7 × 8/100)
= $5550 + (38850 × 8/100)
= $5550 + (310800/100)
= $5550 + $3108 = $8658
Thus, Amount (A) to be paid = $8658 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 $5550, the simple interest in 1 year
= 7/100 × 5550
= 7 × 5550/100
= 38850/100 = $388.5
Thus, simple interest for 1 year = $388.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $388.5 × 8 = $3108
Thus, Simple Interest (SI) = $3108
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $3108
= $8658
Thus, Amount to be paid = $8658 Answer
Similar Questions
(1) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.
(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 8 years.
(4) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?
(5) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 4 years.
(7) If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.
(9) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 7 years.